Selberg integrals and Hankel determinants

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 formula...

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Veröffentlicht in:	Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings vol. AT,...; H. Proceedings; S. 549 - 560
Hauptverfasser:	Ishikawa, Masao, Zeng, Jiang
Format:	Journal Article Tagungsbericht
Sprache:	Englisch
Veröffentlicht:	DMTCS 01.01.2014 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science
Schriftenreihe:	DMTCS Proceedings
Schlagworte:	[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Combinatorics Computer Science Discrete Mathematics hankel determinants hyperpfaffians Mathematics orthogonal polynomials pfaffians Pfaffians hyperpfaffians Orthogonal polynomials Hankel determinants
ISSN:	1365-8050, 1462-7264, 1365-8050
Online-Zugang:	Volltext
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Zusammenfassung:	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. Dans nos travaux précédents “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) nous avons proposé plusieurs méthodes pour évaluer certains Catalan–Pffafian déterminants de Hankel et avons aussi formulé plusieurs conjectures. Dans ce travail nous proposons une nouvelle approche pour calculer ces Catalan-Pffafian déterminants de Hankel en utilisant l’intégrale de Selberg ainsi que leurs $q$-analogues. En particulier, cette approche nous permet de confirmer la plus part de nos conjectures précédentes.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.2422