Masao Ishikawa

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Publications

• Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa and Jiang Zeng, A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials, Proc. Amer. Math. Soc. 143 (2015), 2003-2015.

• Masao Ishikawa and Soichi Okada, "Identities for determinants and Pfaffians, and their applications", Sugaku Expositions 27 (2014), 85-116.

• Masao Ishikawa, Masahiko Ito and Soichi Okada, "A compound determinant identity for rectangular matrices and determinants of Schur functions", Adv. in Appl. Math. 51 (2013), 635-654.

• Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng, "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants", J. Combin. Theory Ser. A 120 (2013), 1263-1284.

• Masao Ishikawa and Soichi Okada, "Equalities and representation theory related to determinants and Pfaffians, and their applications to combinatorics." (Japanese), Sugaku 62 (2010), 85-114.

• Masao Ishikawa and Jiang Zeng, "The Andrews-Stanley Partition Function and Al-Salam-Chihara Polynomials", math.CO/0506128, Descrete Math. 309 (2009), pp. 151-175.

• Masao Ishikawa, Hiroyuki Tagawa and Jiang Zeng, "A q-analogue of Catalan Hankel determinants" (New trends in combinatorial representation theory, Res. Inst. Math. Sci.), RIMS Kokyuroku Bessatsu, B11 (2009), 19-41.

• Masao Ishikawa, Anisse Kasraoui and Jiang Zeng, "Statistics on Ordered Partitions of Sets and q-Stirling Numbers", math.CO/0605390, SIAM J. Discrete Math. 22 (2008), pp. 1105 - 1137. a detailed version.

• Masao Ishikawa, "Minor summation formula and a proof of Stanley's open problem", math.CO/0408204, Ramanujan J. 16 (2008), pp. 211 - 234.

• Masao Ishikawa, Anisse Kasraoui and Jiang Zeng, "EulerMahonian statistics on ordered partitions and Steingrimsson's conjecture - a survey" (Combinatorial representation theory and related topics, Res. Inst. Math. Sci.), RIMS Kokyuroku Bessatsu, B8 (2008), 99-113.

• Masao Ishikawa, Hiroyuki Tagawa, Soichi Okada and Jiang Zeng, "Generalizations of Cuachy's determinant and Schur's Pfaffian", math.CO/0411280, Adv. in Appl. Math. 36, (2006) 251 - 287.

• Masao Ishikawa, Frederic Jouhet and Jiang Zeng, "A generalization of Kawanaka's identity for Hall-Littlewood polynomials and applications", math.CO/0401252, J. Algebraic Combin. 23, (2006) 395 - 412.

• Masao Ishikawa and Masato Wakayama, "Applications of Minor Summation Formula III, Plucker Relations, Lattice Paths and Pfaffian Identities", math.CO/0312358, J. Combin. Theory Ser. A. 113, (2006) 113-155.

• Masao Ishikawa, Hiroyuki Kawamuko and Soichi Okada, "A Pfaffian-Hafnian analogue of Borchardt's identity", math.CO/0408364, Electron. J. Combin. 12(1), (2005) #N9.

• Manabu Hagiwara, Masao Ishikawa and Hiroyuki Tagawa, "A Characterization of the Simply-Laced FC-Finite Coxeter Groups", Ann. Comb. 8, (2004) 177-196.

• Masao Ishikawa and Masato Wakayama, "Minor Summation Formulas of Pfaffians, Survey and A New Identity", Adv. Stud. Pure Math. 28, (2000) 133-142.

• Masao Ishikawa and Masato Wakayama, "Application of Minor-Summation Formula II. Pfaffians and Schur Polynimials'' , J. Combin. Theory Ser. A, 88, (1999), 136-157.

• Masao Ishikawa and Masato Wakayama, "New Schur Function Series", J. Algebra 208 (1998), 480-525.

• Masao Ishikawa, Soichi Okada and Masato Wakayama, "Application of Minor-Summation Formula I. Littlewood's Formulas" , J. Algebra 183 (1996), 193-216.

• Masao Ishikawa and Masato Wakayama, "Minor Summation Formula of Pfaffians", Linear and Multilinear Algebra 39, (1995), 285-296.

• Masao Ishikawa and Masato Wakayama, "Minor Summation of Pfaffians and Scur Function Identities", Proc. Japan Acad. Ser. A Math. Sci. 71 (1995), 54-57 A3.

Preprints

• Takahiro Hayata and Masao Ishikawa "An elementary proof of a binomial-coefficient identity arising from the middle discrete series of SU(2,2)", preprint (April 24, 2008 version), arXiv:0804.3841.

• Masao Ishikawa, "On Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions II", math.CO/0606082.

• Masao Ishikawa, "On Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions I", math.CO/0602068.

Conference Proceedings

• Masao Ishikawa and Jiang Zeng, "Selberg integrals and Catalan-Pfaffian Hankel determinants", Proceedings of the 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'14) (Discrete Math. Theor. Comput. Sci. Proc., AT), (2014), 549-560, poster1, poster2.

• Masao Ishikawa, Hiroyuki Tagawa and Jiang Zeng, "A generalization of Mehta-Wang determinant and Askey-Wilson polynomials", Proceedings of the 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'13), (Discrete Math. Theor. Comput. Sci. Proc., AS), (2013), 719-730, poster1, poster2.

• Masao Ishikawa, "(q,t)-hook formula for Birds", (Algebraic Combinatorics related to Young diagram and statistical physics) RIMS Kokyuroku 1913, (2014) 47-66.

• Masao Ishikawa and Hiroyuki Tagawa, "Leaf posets and multivariate hook length property", (Algebraic Combinatorics related to Young diagram and statistical physics) RIMS Kokyuroku 1913, (2014) 67-80.

• Masao Ishikawa, "Hankel Pfaffian and Selberg integral" (in Japanese), (Perspectives of Representation Theory and Noncommutative Harmonic Analysis) RIMS Kokyuroku 1825, (2013) 103-119.

• Masao Ishikawa and Christoph Koutschan, "Zeilberger's holonomic ansatz for Pfaffians", ISSAC 2012 - Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (2012), pp. 227-233.

• Masao Ishikawa, "A Pfaffian analogue of the Hankel determinants and the Selberg integrals" (in Japanese), (Topics in Combinatorial Representation Theory) RIMS Kokyuroku 1795, (2012) 189-203.

• Masao Ishikawa, "A Pfaffian analogue of q-Catalan Hankel determinants and its application" (in Japanese), (Combinatorial Representation Theory and its Applications) RIMS Kokyuroku 1738, (2011) 102-119.

• Masao Ishikawa, "Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Constant Term Identities", Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'07) Nankai University, Tianjin, China July 2 - 6, (2007).

• Masao Ishikawa and Hiroyuki Tagawa, "Schur Function Identities and Hook Length Posets", Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'07) Nankai University, Tianjin, China July 2 - 6, (2007).

• Masao Ishikawa, Anisse Kasraoui and Jiang Zeng, "Computing generating functions of ordered partitions with the transfermatrix method", (Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, Discrete Math. Theor. Comput. Sci. Proc., AG, (2006), 193-202, a detailed version.

• Masao Ishikawa and Jiang Zeng, "The Partition Function of Andrews and Stanley and Al-Salam-Chihara Polynomials", Proceedings of the 18th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'06). San Diego, California, USA; June 19 - 23, (2006)

• Masao Ishikawa, "A proof of Stanley's open problem", Proceedings of the 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05). (2005) 219 - 230 , Taormina, Sicily, Italy; 20 - 25 June 2005

• Masao Ishikawa, Hiroyuki Tagawa, Soichi Okada and Jiang Zeng, "Generalizations of Cuachy's determinant and Schur's Pfaffian", Proceedings of the 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05). (2005) 231 - 242, Taormina, Sicily, Italy; 20 - 25 June (2005)

• Manabu, Hagiwara, Masao Ishikawa and Hiroyuki Tagawa, "A characterization of the simply-Laced FC-finite Coxeter groups", Proceedings of the 16th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'04) (2004) 107 - 114, University of British Columbia, (Vancouver, Canada), June 28 - July 2, 2004.

• Masao Ishikawa and Hiroyuki Tagawa, "Determinants and Pfaffians associated with d-complete posets", (Topics in Young diagrams and representation theory), RIMS Kokyuroku 1262, (2002) 101-136. (in Japanese).

• Masao Ishikawa, "Pfaffians, Determinants, Young diagrams and hook formulas", Proceedings of the 39th Joint Symposium og Real Function Theory and Functional Analysis, (2000) 63 - 80, Shinshu University, Nagano, Japan.

• Masao Ishikawa and Hiroyuki Tagawa, "A Combinatorial Proof of Hook Length Property of the d-Complete Posets", Proceedings of the 16th Algebraic Combinatorics Symposium, (1999) 123 - 133, Kyushu University, Fukuoka, Japan.

• Masao Ishikawa, "Minor summation formula of Pfaffians and Schur function identities", Proceedings of the 7th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'95), (1995) 379-386, Marne-la-Vallee, France.

• Masao Ishikawa and Masato Wakayama, "Minor summation formula and applications, discrete Fourier transforms", RIMS Kokyuroku 933, (1995) 85 - 104.

• Masao Ishikawa, "A Mixed Knuth Correspondence for (A,B)-Partially Strict Tableaux", (Groups and Combinatorics), RIMS Kokyuroku 794, (1992) 61 - 72.

• Masao Ishikawa, "Number of the self-complementary plane partitions", (Combinatorial Theory and Related Topics - Mutual Relation among Commutative Algebra,Algebraic Geometry,Representation Theory of Lie Algebras and Partially Ordered Sets), RIMS Kokyuroku 670, (1988) 197 - 232, (in Japanese).

Recent Talks

• Masao Ishikawa, Fumihiko Nakano, Taizo Sadahiro and Hiroyuki Tagawa, Domino tilings of Aztec rectangle with connected holes, RIMS Workshop "Combinatorial Representation Theory and Related Topics", October 21, 2015, RIMS, Kyoto University

• Masao Ishikawa, The domino tilings of Aztec rectangles with consecutive holes and the Gauss hypergeometric series, NIMS Thematic Program: 2015 Combinatorics Workshop, July 16, 2015, NIMS - National Institute for Mathematical Sciences (Daejeon, Korea)

• Masao Ishikawa, (q, t)-hook formula for d-complete posets, NIMS Seminar, July 3, 2015, 2015, NIMS - National Institute for Mathematical Sciences (Korea).

• Masao Ishikawa and Jiang Zeng, Selberg integrals and evaluations of Pfaffians, The 73rd Seminaire Lotharingien de Combinatoire, September 8-10, 2014, Bundesinstitut fur Erwachsenenbildung, Strobl (Austria).

• Masao Ishikawa and Jiang Zeng, Selberg integrals and Catalan-Pfaffian Hankel determinants , The 19th International Linear Algebra Society Conference (Solidaity in Linear Algebra), August 6-9, 2014, Sungkyunkwan University (Seoul, Korea)

• Masao Ishikawa and Jiang Zeng, Selberg integrals and Catalan-Pfaffian Hankel determinants , The 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), Sunday, June 29 - Thursday, July 3, 2014, DePaul University, Chicago, Illinois. U.S.A.

• Masao Ishikawa Enumeration problems of plane partitions and determinant generating functions, Expansion of Combinatorial Representation Theory, Octorber 7 -- 10, 2008, RIMS, Kyoto University, Kyoto Japan.

• Masao Ishikawa Enumeration problems of plane partitions and Pfaffian (determinant) expressions, Combinatorics and Representation Theory, (The 8th International Conference by the Graduate School of Mathematics, Nagoya University) September 1 - 5, 2008, Graduate School of Mathematics, Nagoya University, Nagoya, Japan.

• Masao Ishikawa Littlewood’s (Cauchy’s) formulae of Schur functions and constant term expressions for the refined enumeration problems of TSSCPPs, Combinatorics and Statistical Physics, May 16 - 30, 2008, ESI, Vienna, Austria.

• Masao Ishikawa An Identity for Compound Determinant and its Application, Korea Advanced Institute of Science and Technology, Februay 22, 2008.

• Masao Ishikawa Hankel determinants of Catalan, Motzkin and Schroder numbers and its q-analogues, Expansion of Combinatorial Representation Theory, RIMS, Kyoto University, Kyoto, Japan, October 23 - 26, 2007.

• Masao Ishikawa Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Lattice Path Combinatorics, 6th International Conference on Lattice Path Combinatorics and Applications East Tennessee State University, Johnson City, TN. United States, July 13, 2007.

• Masao Ishikawa Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Constant Term Identities, The 19th International Conference on Formal Power Series and Algebraic Combinatorics (Contributed Papers) Nankai University, Tianjin, China, July 2, 2007.

• Masao Ishikawa and Hiroyuki Tagawa Schur Function Identities and Hook Length Posets, The 19th International Conference on Formal Power Series and Algebraic Combinatorics (Contributed Posters) Nankai University, Tianjin, China, July 2 - 6, 2007.

• Masao Ishikawa, Anisse Kasraoui and Jiang Zeng , "Euler-Mahonian Statistics of Ordered Partitions", Combinatorial Representation Theory and Related Topics, October 24 - 27, 2006, RIMS, University of Kyoto, organized by Takeshi Suzuki and Toshiyuki Tanisaki.

• Masao Ishikawa and Jiang Zeng The Andrews-Stanley partition function and Al-Salam-Chihara polynomials, 18th International Conference on Formal Power Series & Algebraic Combinatorics (Contributed Posters) June 19-23, 2006, San Diego, California, Catamaran Resort Hotel, Pacific Beach, USA

• "Minor summation formula of Pfaffians and Mills-Robbins-Rumsey conjectures on totally symmetric self-complementary plane partitions", Department of Mathematics, Ryukyu University February 16, 2006

• The refinements of TSSCPP enumeration, Workshop of Combinatorics on q-Series and Partitions (January 5-6, 2006, Institute of Camille Jordan, University of Lyon I)

• Several refined conjectures on TSSCPP and ASM, The World of Combinatorial Representation Theory (November 8-11, 2005, RIMS, Kyoto University)

• Andrews-Stanley partition function and the orthogonal polynomials, KISS2005 (Kasai Integrable Systems Seminar) Octorber 21, 2005, 15:00 - 16:30, Nakmura Laboratory, Kyoto University

• Minor summation formula of Pfaffains and its applications, July 3-4, 2005, Department of Mathematics, Okayama University

• A Proof of Stanley's Open Problem, 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics (June 20 - 25, 2005 - Taormina, Sicily - Italy)

• Minor summation formula and a proof of Stanley's open problem, Combinatoire et Theorie des Nombres (March 25, 2005, Institute of Camille Jordan, University of Lyon I)

• On Refined TSSCPP Conjectures, December 10, 2004, Department of Mathematics, Osaka University

• An open problem of R. P. Stanley on a sum of Schur functions, Conference on Partially Ordered Sets and Algorithms August 23-25, 2004, Tokai University, Takanawa Campus

Contact address:	Department of Mathematics
	Faculty of Science
	Okayama University
	Tsushima, Okayama 700-8530, Japan
Office Phone :	(+81) 86 251 77 84
Fax :	(+81) 86 251 78 02
Email :

Links

• Search me in Arxiv.

• Google me.

• My home page in Okayama University

• My home page in Tottori University

• Symposium on Representation Theory 2016

• Algebraic Combinatorics related to Young diagrams and Statistical Physics

• Combinatoire et Theorie des Nombres, Institut Camille Jordan, Universite Claude Bernard Lyon 1

• Okamoto Lab