Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
type: Item
instance of: scholarly article
title: Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
zbMATH Open document ID: 1467.05009
DOI: 10.37236/9780
author: Gaspard Ohlmann
published in: The Electronic Journal of Combinatorics
publication date: 2021-07-06T00:00:00Z
review text: Summary: In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where \(d=0\). Their values have already been computed by \textit{J. S. Kim} and \textit{D. Stanton} in [J. Math. Anal. Appl. 421, No. 1, 501--520 (2015; Zbl 1302.33017)], however, the proof is not completely combinatorial, which means that an explicit bijection has not been exhibited yet. In this work, we use a new combinatorial approach for the simpler case of Al-Salam-Carlitz, using a sign reversing involution that directly operates on Motzkin path. We then generalize this method to Askey-Wilson polynomials with \(d=0\) only, providing the first fully combinatorial proof for that case.
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33D50
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 7368130
zbMATH Keywords: Askey-Wilson polynomials
zbMATH Keywords: Al-Salam-Carlitz polynomials
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.37236/9780
OpenAlex ID: W3177624604
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description: scientific article; zbMATH DE number 7368130