Selberg integrals and Catalan-Pfaffian Hankel determinants

Masao Ishikawa, Jiang Zeng

Research output: Contribution to journalConference article

Abstract

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.

Original languageEnglish
Pages (from-to)549-560
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
Publication statusPublished - Jan 1 2014
Externally publishedYes
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: Jun 29 2014Jul 3 2014

Keywords

  • Hankel determinants
  • Hyperpfaffians
  • Orthogonal polynomials
  • Pfaffians

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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