Wakayama University · Faculty of Education · 教授

Research keywordskazhdan-lusztig polynomials・Pfaffian analogues・q-catalan Hankel determinants・askey-wilson polynomials・Schur functions・d-complete posets・determinant identities・Aztec rectangle tilings

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• Jeśmanowicz’ conjecture for non-primitive Pythagorean triples2023 · Hidetaka Kitayama, Hiroyuki Tagawa, Keiichi Urahashi
• A generalization of Mehta-Wang determinant and Askey-Wilson polynomials2013 · 石川 雅雄, 田川 裕之, Jiang Zeng
• Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants2013 · 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.
• A q-analogue of Catalan Hankel determinants2009 · Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

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