Negative moments of orthogonal polynomials
-
Published:2023
Issue:
Volume:11
Page:
-
ISSN:2050-5094
-
Container-title:Forum of Mathematics, Sigma
-
language:en
-
Short-container-title:Forum of Mathematics, Sigma
Author:
Jang Jihyeug,Kim Donghyun,Kim Jang Soo,Song Minho,Song U-Keun
Abstract
Abstract
If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference20 articles.
1. [12] Kim, J. S. and Stanton, D. , ‘Combinatorics of orthogonal polynomials of type R I ’, https://arxiv.org/abs/2009.14475.
2. Determinants, paths, and plane partitions;Gessel;Preprint,1989
3. Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications
4. Combinatorial aspects of continued fractions
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献