The combinatorics of Al-Salam-Chihara q-Laguerre polynomials

Anisse Kasraoui; Dennis Stanton; Jiang Zeng

doi:10.1016/j.aam.2010.04.008

The combinatorics of Al-Salam-Chihara q-Laguerre polynomials

Anisse Kasraoui, Dennis Stanton, Jiang Zeng

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We describe various aspects of the Al-Salam-Chihara q-Laguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. It is remarkable that the corresponding moment sequence appears also in the recent work of Postnikov and Williams on enumeration of totally positive Grassmann cells.

Original language	English (US)
Pages (from-to)	216-239
Number of pages	24
Journal	Advances in Applied Mathematics
Volume	47
Issue number	2
DOIs	https://doi.org/10.1016/j.aam.2010.04.008
State	Published - Aug 2011

Bibliographical note

Funding Information:
This work was partially supported by the French National Research Agency under the grant ANR-08-BLAN-0243-03.

Keywords

Al-Salam-Chihara polynomials
Linearization coefficients
q-Laguerre polynomials
y-Version of q-Stirling numbers of the second kind

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AU - Stanton, Dennis

AU - Zeng, Jiang

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AB - We describe various aspects of the Al-Salam-Chihara q-Laguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. It is remarkable that the corresponding moment sequence appears also in the recent work of Postnikov and Williams on enumeration of totally positive Grassmann cells.

KW - Al-Salam-Chihara polynomials

KW - Linearization coefficients

KW - q-Laguerre polynomials

KW - y-Version of q-Stirling numbers of the second kind

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The combinatorics of Al-Salam-Chihara q-Laguerre polynomials

Abstract

Bibliographical note

Keywords

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