Lecture hall graphs and the Askey scheme

Autor:	Corteel, Sylvie, Jonnadula, Bhargavi, Keating, Jonathan P., Kim, Jang Soo
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Mathematical Physics Mathematics - Classical Analysis and ODEs 05A15 (primary) 33D45 05A10 05A19 05A30 (secondary)
Druh dokumentu:	Working Paper
Popis:	We establish, for every family of orthogonal polynomials in the $q$-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph. This generalizes the previous results of Corteel and Kim for the little $q$-Jacobi polynomials. We build these combinatorial models by bootstrapping, beginning with polynomials at the bottom and working towards Askey-Wilson polynomials which sit at the top of the $q$-Askey scheme. As an application of the theory, we provide the first combinatorial proof of the symmetries in the parameters of the Askey-Wilson polynomials. Comment: 43 pages, 23 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.12761 Zobrazit plný text záznamu View this record from Arxiv