Mathematics > Combinatorics
[Submitted on 27 Jan 2022 (v1), last revised 7 Mar 2023 (this version, v2)]
Title:Negative moments of orthogonal polynomials
View PDFAbstract: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.
Submission history
From: Donghyun Kim [view email][v1] Thu, 27 Jan 2022 06:55:06 UTC (28 KB)
[v2] Tue, 7 Mar 2023 06:09:58 UTC (29 KB)
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