Updated on 2021/12/19

写真a

 
ISHIKAWA Masao
 
Organization
Faculty of Natural Science and Technology Professor
Position
Professor
Contact information
メールアドレス
External link

Degree

  • 博士(理学) ( 東京大学 )

Research Interests

  • Plane partition

  • Symmetric Functions

  • Algebraic Combinatorics

  • Alternating sign matrix

  • Determinant

  • Enumerative Combinatorics

  • Pfaffian

  • Representation Thorey

Research Areas

  • Natural Science / Algebra  / Algebraic Combinatorics

  • Natural Science / Algebra  / Representation Theory

Education

  • The University of Tokyo   大学院理学系研究科博士課程   数学専攻

    1988.4 - 1992.3

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  • The University of Tokyo   大学院理学系研究科修士課程   数学専攻

    1986.4 - 1988.3

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Research History

  • Okayama University   Graduate School of Natural Science and Technology   Professor

    2015.4

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  • University of the Ryukyus   Faculty of Education   Professor

    2011.4 - 2015.3

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  • Tottori University   Education Center   Associate Professor

    2010.4 - 2011.3

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  • Tottori University   Education Center   Associate Professor

    2008.4 - 2010.3

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  • Tottori University   University Education Center   Associate Professor

    2007.4 - 2008.3

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  • Tottori University   University Education Center   Associate Professor (as old post name)

    2004.4 - 2007.3

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  • Tottori University   Faculty of Education and Regional Sciences   Associate Professor (as old post name)

    1999.4 - 2003.3

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  • Tottori University   Faculty of Education   Associate Professor (as old post name)

    1995.10 - 1999.3

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  • Tottori University   Faculty of Education   Lecturer

    1995.4 - 1995.9

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  • Tottori University   College of Liberal Arts   Lecturer

    1992.5 - 1995.3

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Professional Memberships

Committee Memberships

  • 日本数学会   代議員(中四国地区)  

    2004.4 - 2005.3   

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    Committee type:Academic society

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Papers

  • Determinant Structure for τ -Function of Holonomic Deformation of Linear Differential Equations Reviewed

    Masao Ishikawa, Toshiyuki Mano, Teruhisa Tsuda

    Communications in Mathematical Physics   363 ( 3 )   1081 - 1101   2018.9

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  • A binomial-coefficient identity arising from the middle discrete series of SU(2,2) Reviewed

    Takahiro Hayata, Masao Ishikawa

    Mathematical Journal of Okayama University   60   221 - 231   2018.1

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  • A QUADRATIC FORMULA FOR BASIC HYPERGEOMETRIC SERIES RELATED TO ASKEY-WILSON POLYNOMIALS Reviewed

    Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   143 ( 5 )   2003 - 2015   2015.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER MATHEMATICAL SOC  

    We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey-Wilson polynomials from Newton's interpolation formula.

    DOI: 10.1090/S0002-9939-2015-12099-0

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  • Selberg integrals and Catalan-Pfaffian Hankel determinants Reviewed

    Masao Ishikawa, Jiang Zeng

    Proceedings of the 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'14), (Discrete Math. Theor. Comput. Sci. Proc., AT)   549 - 560   2014.7

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    File: 4524.pdf

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  • Identities for determinants and Pfaffians, and their applications Reviewed

    Masao Ishikawa, Soichi Okada

    Sugaku Expositions   27   85 - 116   2014

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  • A compound determinant identity for rectangular matrices and determinants of Schur functions Reviewed

    Masao Ishikawa, Masahiko Ito, Soichi Okada

    ADVANCES IN APPLIED MATHEMATICS   51 ( 5 )   635 - 654   2013.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    A compound determinant identity for minors of rectangular matrices is established. Given an (s + n - 1) x sn matrix A with s blocks of n columns, we consider minors of A by picking up in each block the first consecutive columns specified by weak compositions at most s parts, and prove that the compound determinant of such n x n minors of A is equal to the product of maximal minors of A corresponding to compositions of s + n - 1 with s parts. As an application, we obtain Vandermonde type product evaluations of determinants of classical group characters, including Schur functions. (C) 2013 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.aam.2013.08.001

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  • Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants Reviewed

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    JOURNAL OF COMBINATORIAL THEORY SERIES A   120 ( 6 )   1263 - 1284   2013.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Motivated by the Hankel determinant evaluation of moment sequences, we study an analogous Pfaffian evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this formula to evaluate Pfaffians related to some moment sequences of classical orthogonal polynomials. In particular we obtain a product formula for a kind of q-Catalan Pfaffians. We also establish a connection between our Pfaffian formulas and certain weighted enumeration of shifted reverse plane partitions. (C) 2013 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jcta.2013.03.008

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  • A generalization of Mehta-Wang determinant and Askey-Wilson polynomials Reviewed

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    Proceedings of the 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'13),(Discrete Math. Theor. Comput. Sci. Proc., AS)   719 - 730   2013

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    File: 4252.pdf

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  • Zeilberger's holonomic ansatz for pfaffians Reviewed

    Masao Ishikawa, Christoph Koutschan

    Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC   227 - 233   2012

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    A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace expansion (cofactor expansion) of the determinant, we derive our approach from the cofactor expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary. Copyright 2012 ACM.

    DOI: 10.1145/2442829.2442863

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  • Identities for determinants and Pfaffians, and their applications Reviewed

    Masao Ishikawa, Soichi Okada

    Sugaku   62   85 - 114   2010

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  • A q-analogue of Catalan Hankel determinants Reviewed

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    RIMS Kokyuroku Bessatsu   B11   19 - 41   2009.4

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  • The Andrews-Stanley partition function and Al-Salam-Chihara polynomials Reviewed

    Masao Ishikawa, Jiang Zeng

    DISCRETE MATHEMATICS   309 ( 1 )   151 - 175   2009.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    For any partition lambda let omega (lambda) denote the four parameter weight
    omega(lambda) =a(Sigma i >= 1[lambda 2i-1/2])b(Sigma i >= 1[lambda 2i-1/2])c(Sigma i >= 1[lambda 2i/2])d(Sigma i >= 1[lambda 2i/2]).
    and let l(lambda) be the length of lambda. We show that the generating function Sigma omega(lambda)z(l(lambda)), where the sum runs over all ordinary (resp. strict) partitions with parts each <= N, can be expressed by the Al-Salam-Chihara polynomials. As a corollary we derive Andrews' result by specializing some parameters and Boulet's results by letting N -> +infinity. In the last section we prove a Pfaffian formula for the weighted sum Sigma omega(lambda)z(l(lambda)) P(lambda)(x) where P(lambda)(x) is Schur's P-function and the sum runs over all strict partitions. (C) 2008 Published by Elsevier B.V.

    DOI: 10.1016/j.disc.2007.12.064

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  • Minor summation formula and a proof of Stanley's open problem Reviewed

    Masao Ishikawa

    RAMANUJAN JOURNAL   16 ( 2 )   211 - 234   2008.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    In the open problem session of the FPSAC'03, R. P. Stanley gave an open problem about a certain sum of the Schur functions. The purpose of this paper is to give a proof of this open problem. The proof consists of three steps. At the first step we express the sum by a Pfaffian as an application of our minor summation formula (Ishikawa and Wakayama in Linear Multilinear Algebra 39: 285-305, 1995). In the second step we prove a Pfaffian analogue of a Cauchy type identity which generalizes Sundquist's Pfaffian identities (J. Algebr. Comb. 5: 135-148, 1996). Then we give a proof of Stanley's open problem in Sect. 4. At the end of this paper we present certain corollaries obtained from this identity involving the Big Schur functions and some polynomials arising from the Macdonald polynomials, which generalize Stanley's open problem.

    DOI: 10.1007/s11139-007-9106-9

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  • Euler-Mahonian Statistics on Ordered Partitions and Steingrimsson's cojecture --- A survey Reviewed

    Masao Ishikawa, Anisse Kasraoui, Jiang Zeng

    RIMS Kokyuroku Bessatsu   B8   99 - 114   2008.5

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  • Euler-Mahonian statistics on ordered set partitions Reviewed

    Masao Ishikawa, Anisse Kasraoui, Jiang Zeng

    SIAM JOURNAL ON DISCRETE MATHEMATICS   22 ( 3 )   1105 - 1137   2008

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    An ordered partition with k blocks of [n] := {1, 2,..., n} is a sequence of k disjoint and nonempty subsets, called blocks, whose union is [n]. Clearly the number of such ordered partitions is k! S(n, k), where S(n, k) is the Stirling number of the second kind. A statistic on ordered partitions of [n] with k blocks is called an Euler-Mahonian statistic if its generating polynomial is [k](q)!S-q(n, k), which is a natural q-analogue of k! S(n, k). Motivated by Steingrimsson's conjectures dating back to 1997, we consider two different methods to produce Euler-Mahonian statistics on ordered set partitions: (a) we give a bijection between ordered partitions and weighted Motzkin paths by using a variant of Francon-Viennot's bijection to derive many Euler-Mahonian statistics by expanding the generating function of [k](q)!S-q(n, k) as an explicit continued fraction; (b) we encode ordered partitions by walks in some digraphs and then derive new Euler-Mahonian statistics by computing their generating functions using the transfer-matrix method. In particular, we prove several conjectures of Steingrimsson.

    DOI: 10.1137/060672340

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  • Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Constant Term Identities Reviewed

    Masao Ishikawa

    Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'07)   2007.6

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    File: fpsac07a.pdf

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  • Schur Function Identities and Hook Length Posets Reviewed

    Masao Ishikawa, Hiroyuki Tagawa

    Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'07)   2007.6

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  • The Partition Function of Andrews and Stanley and Al-Salam-Chihara Polynomials Reviewed

    Masao Ishikawa, Jiang Zeng

    Proceedings of the 18th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'06)   2006.6

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  • A generalization of Kawanaka's identity for Hall-Littlewood polynomials and applications Reviewed

    M Ishikawa, F Jouhet, J Zeng

    JOURNAL OF ALGEBRAIC COMBINATORICS   23 ( 4 )   395 - 412   2006.6

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    An infinite summation formula of Hall-Littlewood polynomials due to Kawanaka is generalized to a finite summation formula, which implies, in particular, twelve more multiple q-identities of Rogers-Ramanujan type than those previously found by Stembridge and the last two authors.

    DOI: 10.1007/s10801-006-8350-1

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  • Generalizations of Cauchy's determinant and Schur's pfaffian Reviewed

    M Ishikawa, S Okada, H Tagawa, J Zeng

    ADVANCES IN APPLIED MATHEMATICS   36 ( 3 )   251 - 287   2006.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We present several identities of Cauchy-type determinants and Schur-type Pfaffians involving generalized Vandermonde determinants, which generalize Cauchy's determinant det(1 /(x(i) + y(j))) and Schur's Pfaffian Pf((x(j) - x(i))/(x(j) + x(i))). Some special cases of these identities are given by S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood-Richard son coefficients involving a rectangular partition. (c) 2005 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.aam.2005.07.001

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  • Applications of minor summation formula III, Pluicker relations, lattice paths and Pfaffian identities Reviewed

    M Ishikawa, M Wakayama

    JOURNAL OF COMBINATORIAL THEORY SERIES A   113 ( 1 )   113 - 155   2006.1

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    The initial purpose of the present paper is to provide a combinatorial proof of the minor summation formula of Pfaffians in [Ishikawa, Wakayama, Minor summation formula of Pfafflans, Linear and Multilinear Algebra 39 (1995) 285-305] based on the lattice path method. The second aim is to study applications of the minor summation formula for obtaining several identities. Especially, a simple proof of Kawanaka's formula concerning a q-series identity involving the Schur functions [Kawanaka, A q-series identity involving Schur functions and related topics, Osaka J. Math. 36 (1999) 157-176] and of the identity in [Kawanaka, A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups, Osaka J. Math. 38 (2001) 775-810] which is regarded as a determinant version of the previous one are given. (c) 2005 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jcata.2005.05.008

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  • Computing generating functions of ordered partitions with the transfer-matrix method Reviewed

    Masao Ishikawa, Anisse Kasraoui, Jiang Zeng

    Discrete Math. Theor. Comput. Sci. Proc.( Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities)   193 - 202   2006

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  • A Pfaffian-Hafnian analogue of Borchardt's identity Reviewed

    M Ishikawa, H Kawamuko, S Okada

    ELECTRONIC JOURNAL OF COMBINATORICS   12 ( 1 )   N9   2005.6

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    We prove
    Pf (x(i)-x(j)/(x(i)-x(j))(2))(1 <= i,j <= 2n) = Pi 1 <= i < j <= 2n x(i)-x(j)/x(i)-x(j) (.) Hf (1/x(i)+x(j))(1 <= i,j <= 2n)
    (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.

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  • Generalizations of Cauchy's Determinant and Schur's Pfaffian Reviewed

    Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa, Jiang Zeng

    Proceedings of the 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05)   231 - 242   2005.6

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  • A Proof of Stanley's Open Problem Reviewed

    Masao Ishikawa

    Proceedings of the 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05)   219 - 230   2005.6

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  • A characterization of the simply-Laced FC-finite Coxeter groups Reviewed

    Manabu Hagiwara, Masao Ishikawa, Hiroyuki Tagawa

    Annals of Combinatorics   8   177 - 196   2004

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  • Minor summation formulas of pfaffians, survey and a new identity Reviewed

    M Ishikawa, M Wakayama

    COMBINATORIAL METHODS IN REPRESENTATION THEORY   28   133 - 142   2000

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    In this paper we treat the minor summation formulas of pfaffians presented in [IW1] and derive several basic formulas concerning pfaffians from it. We also present a pfaffian version of the Plucker relation and give a new pfaffian identity as its application.

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  • Applications of minor-summation formula II. Pfaffians and Schur polynomials Reviewed

    M Ishikawa, M Wakayama

    JOURNAL OF COMBINATORIAL THEORY SERIES A   88 ( 1 )   136 - 157   1999.10

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    The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (lshikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof. we present an open problem which generalizes our formula. (C) 1999 Academic Press.

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  • New Schur function series Reviewed

    M Ishikawa, M Wakayama

    JOURNAL OF ALGEBRA   208 ( 2 )   480 - 525   1998.10

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    This paper presents some new product identities for certain summations of Schur functions. These identities are generalizations of some famous identities known to Littlewood and appearing in Macdonald's book. We refer to these identities as the "Littlewood-type formulas." In addition, analogues for summations of characters of the other classical groups are also given. The Littlewood-type formulas in this paper are separated into two classes, the rational Schur function series and the generalized Schur function series. An application of a rational Schur function series to the infinite product representation of the elliptic theta functions is also given. We prove these Littlewood-type formulas using the Cauchy-Binet formula. The Cauchy-Binet formula is a basic but powerful tool applicable in the present context, which can be derived from our Pfaffian formula, as we explain. (C) 1998 Academic Press.

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  • Applications of minor-summation formula .1. Littlewood's formulas Reviewed

    M Ishikawa, S Okada, M Wakayama

    JOURNAL OF ALGEBRA   183 ( 1 )   193 - 216   1996.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS  

    The first and the third authors obtained a minor-summation formula of Pfaffian, which expresses a weighted sum of miners of any rectangular matrix in terms of a single Pfaffian. In this paper, as an application of this minor-summation formula, we give a new proof of Littlewood's formulas with additional parameters and generalize them for the classical groups. (C) 1996 Academic Press, Inc.

    DOI: 10.1006/jabr.1996.0214

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  • Minor summation formula of pfaffians and Schur functions identities Reviewed

    Masao Ishikawa

    Proceedings of the 7th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'95)   379 - 386   1995.6

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  • MINOR SUMMATION FORMULA OF PFAFFIANS AND SCHUR FUNCTION IDENTITIES Reviewed

    M ISHIKAWA, M WAKAYAMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   71 ( 3 )   54 - 57   1995.3

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  • Minor summation formula of Pfaffians Reviewed

    Masao Ishikawa, Masato Wakayama

    Linear and Multilinear Algebra   39   285 - 305   1995

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Books

  • 社会・環境と健康 (スタンダード栄養・食物シリーズ)

    大塚譲, 山根千幸, 石川雅雄( Role: Contributor ,  第16章「情報処理」)

    東京化学同人  2003.6 

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MISC

  • Hankel type Pfaffians and the associated Jacobi polynomials (Recent advances in combinatorial representation theory)

    Masao Ishikawa

    RIMS Kôkyûroku   2183   2021.4

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  • Algebraic aspects of binomial coefficient

    Masao Ishikawa

    Sugaku seminar   705   2020.7

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  • Several classes of plane partitions with the same generating function (Representation Theory and its Combinatorial Aspects)

    Masao Ishikawa

    RIMS Kôkyûroku   2161   73 - 80   2020.6

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  • Generating function on a certain class of plane partitions

    Masao Ishikawa

    RIMS Kôkyûroku   2127   105 - 115   2019.9

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  • Domino tilings of Aztec rectangles with connected holes

    Masao Ishikawa, Fumihiko Nakana, Taizo Sadahiro, Hiroyuki Tagawa

    RIMS Kôkyûroku   1992   114 - 125   2016.4

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  • An extension of Wilson's Gram determinants

    Masao Ishikawa, Hiroyuki Tagawa

    RIMS Kôkyûroku   1945   38 - 53   2015.4

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  • Leaf posets and multivariate hook length property

    Ishikawa Masao

    RIMS Kôkyûroku   1913   67 - 80   2014.8

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  • (q,t)-hook formula for Birds

    Ishikawa Masao

    RIMS Kôkyûroku   1913   47 - 66   2014.8

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  • Hankel Pfaffians and Selberg Integrals

    Ishikawa Masao

    RIMS Kôkyûroku   1825   103 - 119   2013.2

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  • Hankel Pfaffian とSelberg 積分 (表現論と非可換調和解析の展望)

    石川 雅雄

    数理解析研究所講究録   1825   103 - 119   2013.2

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    Language:Japanese   Publisher:京都大学  

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    Other Link: http://hdl.handle.net/2433/194741

  • A Pfaffian analogue of the Hankel determinants and the Selberg integrals

    Masao Ishikawa, Jiang Zeng

    RIMS Kôkyûroku   1795   189 - 203   2012.5

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  • A generalization of the Mehta-Wang determinant and the Askey-Wilson polynomials

    Masao Ishikawa, Hiroyuki Tagawa

    RIMS Kôkyûroku   1795   204 - 223   2012.5

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  • A Pfaffian analogue of q-Catalan Hankel determinants and its application (Combinatorial Representation Theory and its Applications)

    Masao Ishikawa, Hiroyuki Tagawa

    RIMS Kôkyûroku   1738   112 - 119   2011.4

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  • 代数的組合せ論 (特集 [入門]組合せ論)

    石川 雅雄

    数学セミナー   45 ( 11 )   32 - 36   2006.11

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    Language:Japanese   Publisher:日本評論社  

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  • Determinants and Pfaffians associated with d-complete posets

    Masao Ishikawa, Hiroyuki Tagawa

    RIMS Kôkyûroku   1262   101 - 136   2002.5

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  • Pfaffians, Determinants, Young diagrams and hook formulas

    Ishikawa Masao

    63 - 80   2000

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  • A Combinatorial Proof of Hook Length Property of the d-Complete Posets

    Masao Ishikawa, Hiroyuki Tagawa

    123 - 133   1999

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  • Minor summation formula and applications, discrete Fourier transforms

    Masao Ishikawa, Masato Wakayama

    RIMS Kôkyûroku   933   85 - 104   1995.12

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  • Mixed Robinson-Shensted correspondence, Fomin version, and mixed Kunth correspondence for (A,B)-partially strict tableaux

    Masao Ishikawa

    The Journal of the Faculty of Education, Tottori University. Natural science   44   17 - 64   1995.6

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  • Remarks on Totally Symmetric Self-Complementary Plane Partitions

    Masao Ishikawa

    The Journal of the Faculty of Education, Tottori University. Natural science   44 ( 1 )   65 - 89   1995.6

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  • Minor summation formula of Pfaffians and Schur function identities

    Masao Ishikawa

    The journal of the Faculty of General Education   28   107 - 123   1994.6

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  • A Mixed Knuth Correspondence for (A,B)-Partially Strict Tableaux

    Ishikawa Masao

    RIMS Kôkyûroku   794   61 - 72   1992.6

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  • On the number of self-complementary plane partitions

    Ishikawa Masao

    RIMS Kôkyûroku   670   197 - 232   1988.9

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Presentations

  • Hankel type Pfaffians and the associated Jacobi polynomials Invited

    Masao Ishikawa

    Symposium on Algebraic Combinatorics  2021.6.14 

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    Event date: 2021.6.14 - 2021.6.16

    Language:Japanese   Presentation type:Oral presentation (keynote)  

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  • Hankel type Pfaffians and the associated Jacobi polynomials

    Masao Ishikawa

    Recent advances in combinatorial representation theory  2020.10.7 

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    Event date: 2020.10.5 - 2020.10.8

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Enumeration of alternating sign matrices and plane partitions and Hankel determinants Invited

    Masao Ishikawa

    JCCA2020-DMIA2020-SGT9  2020.8.18 

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    Event date: 2020.8.18 - 2020.8.20

    Language:Japanese   Presentation type:Oral presentation (keynote)  

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  • Distributive Lattice of Half-Turn Symmetric Alternating Sign Matrices

    Masao Ishikawa

    Representation Theory and its Combinatorial Aspects  2019.10.29 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Distributive Lattice of Half-Turn Symmetric Alternating Sign Matrices

    Masao Ishikawa

    2019.9.10 

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  • Several classes of plane partitions with the same generating function

    Masao Ishikawa

    Aspects of Combinatorial Representation Theory  2018.10.11  Daisuke Sagaki (Tsukuba University)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • (q, t)-hook formula for Tailed Insets and a Macdonald polynomial identity International conference

    Masao Ishikawa

    Algebraic and Enumerative Combinatorics in Okayama  2018.2.23  Masao Ishikawa

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Graduate School of Natural Science and Technology, Okayama University  

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  • Leaf poset and multi-colored hook length property

    Masao Ishikawa

    S´eminaire de Combinatoire et Th´eorie des Nombres  2017.9.26  Philippe Nadeau

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institut Camille Jordan, Universite Claude Bernard Lyon 1 (France)  

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  • Domino tilings of Aztec rectangle with connected holes

    Masao Ishikawa

    RIMS Workshop "Combinatorial Representation Theory and Related Topics"  2015.10.21  Katsuyuki Naoi (Tokyo University of Agriculture and Technology)

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • The domino tilings of Aztec rectangles with consecutive holes and the Gauss hypergeometric series International conference

    Masao Ishikawa

    NIMS 2015 Combinatorics Workshop  2015.7.16 

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:National Institute for Mathematical Sciences, Daejeon, Korea  

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  • (q, t)-hook formula for d-complete posets International conference

    Masao Ishikawa

    NIMS Seminar  2015.7.3 

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:National Institute for Mathematical Sciences, Daejeon, Korea  

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  • Selberg Integrals and Evaluations of Hyperpfaffians

    Masao Ishikawa

    RIMS workshop Representation theory and related combinatorics  2014.10.31  Yasuhide Numata (Shinshu University)

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • Selberg integrals and Catalan-Pfaffian Hankel determinants

    Masao Ishikawa

    Le Seminaire de Theorie des Nombres et Combinatoire  2014.9.17  Philippe Nadeau

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Universite Claude Bernard Lyon 1 (France)  

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  • Selberg integrals and evaluations of Pfaffians International conference

    Masao Ishikawa

    The 73rd Seminaire Lotharingien de Combinatoir  2014.9.10  Christian Krattenthaler

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Bundesinstitut f ¨ur Erwachsenenbildung, Strobl, Austria  

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  • Selberg integrals and evaluations of Pfaffians Invited International conference

    Masao Ishikawa

    The 19th International Linear Algebra Society Conference, “Solidaity in Linear Algebra”  2014.8.8 

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Sungkyunkwan University, Korea  

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  • (q, t)-hook formula for Birds and Banners International conference

    Masao Ishikawa

    Bethe Ansatz, Quantum Groups and Beyond  2013.3.9 

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Research Institute for Mathematical Sciences, Kyoto University  

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  • (q, t)-hook formula for Birds International conference

    Masao Ishikawa

    Algebraic Combinatorics related to Young diagram and statistical physics  2012.8.10  Masao Ishikawa

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:International Institute for Advanced Study (Kizugawa, Kyoto)  

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  • A Partial Proof of Okada's (q,t)-Hook Formula Conjecture for Birds

    Masao Ishikawa

    Seminar on analysis of combinatorial structures and its applications for information theory  2011.8.9  Manabu Hagiwara

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Ashikaga, Tochigi  

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  • A Pfaffian analogue of q -Catalan Hankel determinants and its application

    Masao Ishikawa

    Combinatorial Representation Theory and its Applications  2010.10.21  Sho Matsumoto (Nagoya University)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • Fully commutative elements, fully covering elements and d-complete posets Invited

    Masao Ishikawa

    Seminar on analysis of combinatorial structures and its applications for information theory  2010.8.7  Manabu Hagiwara

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Ashikaga, Tochigi  

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  • A partial proof of Okada's conjecture for double-tailed diamonds International conference

    Masao Ishikawa

    64th Séminaire Lotharingien de Combinatoire  2010.3.30 

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institut Camille Jordan - Bâtiment Braconnier Université Claude Bernard Lyon, France  

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  • Enumeration Problem of Certain classes of FPLs and Plane Partitions

    Masao Ishikawa

    Combinatorics Summer School 2009 (COS 2009)  2009.9.2  Yasuhide Numata

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Wakkanai Hokusei Gakuen University  

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  • Enumeration problems of plane partitions and determinant generating functions

    Masao Ishikawa

    Expansion of Combinatorial Representation Theory  2008.10.9  Hyohe Miyachi (Nagoya University)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • Enumeration problem of plane partitions and determinants, Pfaffians Invited

    Masao Ishikawa

    Combinatorics Summer School 2008 (COS 2008)  2008.9.8  Manabu Hagiwara

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Culture Resort Festone, Okinawa, Japan.  

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  • Enumeration problems of plane partitions and Pfaffian (determinant) expressions Invited International conference

    Masao Ishikawa

    Combinatorics and Representation Theory  2008.9.4 

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Graduate School of Mathematics, Nagoya University  

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  • Littlewood ’s (Cauchy ’s) formulae of Schur functions and constant term expressions for the re ned enumeration problems of TSSCPPs Invited International conference

    Masao Ishikawa

    Combinatorics and Statistical Physics  2008.5.27  Mireille Bousquet-Mélou, Michael Drmota, Christian Krattenthaler, Bernard Nienhuis

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:The ERWIN SCHRÖDINGER INTERNATIONAL INSTITUTE for MATHEMATICAL PHYSICS, Vienna, Austria  

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  • Hankel determinants of Catalan, Motzkin and Schroder numbers and its q-analogues

    Masao Ishikawa

    2007.10.24  Masato Okado

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • Hankel determinants of Catalan, Motzkin and Schroder numbers and its q-analogues

    Masao Ishikawa

    Combinatorics Summer School 2007 (COS 2007)  2007.9.3  Masahiro Hachimori (University of Tsukuba)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Okinawa, Japan  

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  • Refi ned Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Lattice Path Combinatorics International conference

    Masao Ishikawa

    6th International Conference on Lattice Path Combinatorics and Applications  2007.6.13 

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:East Tennessee State University, Johnson City, TN, United States  

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  • Re fined enumerations of totally symmetric self-complementary plane partitions and constant term Identities International conference

    Masao Ishikawa

    19th International Conference on Formal Power Series and Algebraic Combinatorics  2007.6.2  Bill Chen (Nankai University, China)

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Nankai Uni- versity, Tianjin, China  

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  • Euler-Mahonian Statistics of Ordered Partitions

    Masao Ishikawa

    Combinatorial Representation Theory and Related Topics  2006.10.25  Takeshi Suzuki (Kyoto University)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:RIMS, Kyoto University  

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  • The re nements of TSSCPP enumeration Invited International conference

    Masao Ishikawa

    Workshop of Combinatorics on q-Series and Partitions  2006.1.5  Jiang Zeng

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Salle 112, 1er étage, Bâtiment Jean Braconnier Institut Camille Jordan, Lyon, France  

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  • Several re ned conjectures on TSSCPP and ASM

    Masao Ishikawa

    The World of Combinatorial Representation Theory  2005.11.8  Hiroshi Mizukawa (Depertment of Mathematics, National Defense Academy in Japan)

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Research Institute for Mathematical Sciences, Kyoto University  

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  • A Proof of Stanley's Open Problem International conference

    Masao Ishikawa

    The 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05)  2005.6.22  Luisa Carini

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Taormina, Sicily, Italy  

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  • Minor summation formula and a proof of Stanley's open problem

    Masao Ishikawa

    Combinatoire et Theorie des Nombres  2005.3.25  Jiang Zeng

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institute of Camille Jordan, University of Lyon I, France  

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  • R. P. Stanley's open problem on the Schur functions

    Masao Ishikawa

    Partially Ordered Sets and Algorithms  2004.8.25 

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    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Tokai University Junior College  

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  • Minor summation formula of pfaffians and Schur func-tions identities International conference

    Masao Ishikawa

    The 7th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'95)  1995.6  Jacques Désarménien

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    Language:English   Presentation type:Oral presentation (general)  

    Venue:Marne-la- Vallee, France  

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Awards

  • Inoue Research Award for Young Scientists

    1992  

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  • 井上研究奨励賞

    1992  

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    Country:Japan

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Research Projects

  • Algebraic combinatorics of symmetric functions and its expansion to representation theory and enumerative combinatorics

    2018.04 - 2021.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Soichi Okada

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    Grant type:Competitive

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  • Study of enumeration of plane partitions and tilings, symmetric functions, determinants and Pfaffians

    2016.04 - 2019.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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  • Study of combinatorics of alternating sign matrices and plane partitions, determinants and Pfaffians

    2013.04 - 2016.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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  • Study of algebraic combinatorics of plane partitions and alternating sign matrices and related representation theory and theoretical physics

    2012.04 - 2017.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (B) 

    Soichi Okada

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    Grant type:Competitive

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  • Determinants and Pfaffians appearing in enumeration of plane partitions and theoretical physics

    2009.04 - 2012.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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  • Study of determinants, Pfaffians and q-series appearing in enumeration problems

    2007.04 - 2009.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Combinatorics of alternating sign matrix and symmetric functions and their applications to representation theory and integrable system

    2006.04 - 2009.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Soichi Okada

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  • Study of enumeration of plane partitions and associated determinants and Pfaffians with hyper geometric identities

    2005.04 - 2007.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Study of character type formula for d-complete posets with the symmetric functions

    2001.04 - 2003.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Littlewood type identity and its applications

    1997.04 - 2000.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Study of duality and "infinite sum=infinite product" type formula from the aspect of the trace formula

    1997.04 - 1999.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (B) 

    Masato Wakayama

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    Grant type:Competitive

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  • Multi-aspect study of G-function

    1996.04 - 1997.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Takashi Harase

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    Grant type:Competitive

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  • Minor summation formula of Pfaffians and applications to the characters of the classical groups

    1995.04 - 1996.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Young Scientists (A) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Harmonic analysis in symmetric space and its applications

    1995.04 - 1996.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Keisaku Kumahara

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    Grant type:Competitive

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  • Minor summation formula of Pfaffians and applications to the representation theory and combinatorics

    1994.04 - 1995.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Young Scientists (A) 

    Masao Ishikawa

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    Authorship:Principal investigator  Grant type:Competitive

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  • Harmonic analysis based on quantum symmetry and its applications

    1993.04 - 1994.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masato Wakayama

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    Grant type:Competitive

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  • Study of second differential form in Riemannian space

    1992.04 - 1993.03

    Japan Society for the Promotion of Science  Grant-in-Aid for Scientific Research (C) 

    Masatoshi Kojima

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    Grant type:Competitive

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Class subject in charge

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  • Theory of Representations (2020academic year) Late  - その他

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Media Coverage

  • Mathematical Journal of Okayama University Promotional material

    Department of Mathematics, Faculty of Science, Okayama University  Mathematical Journal of Okayama University  2017.1

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