## Ishikawa, Masao and Zeng, Jiang - Selberg integrals and Hankel determinants

dmtcs:2422 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Selberg integrals and Hankel determinants

Authors: Ishikawa, Masao and Zeng, Jiang

In our previous works "Pfaffian decomposition and a Pfaffian analogue of $q$-Catalan Hankel determinants'' (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser. A, 120, 2013, 1263-1284) we have proposed several ways to evaluate certain Catalan-Hankel Pffafians and also formulated several conjectures. In this work we propose a new approach to compute these Catalan-Hankel Pffafians using Selberg's integral as well as their $q$-analogues. In particular, this approach permits us to settle most of the conjectures in our previous paper.

Source : oai:HAL:hal-01207553v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: Hankel determinants,Pfaffians,hyperpfaffians,Orthogonal polynomials,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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