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

Anisse Kasraoui, Dennis Stanton, Jiang Zeng

Research output: Contribution to journalArticlepeer-review

10 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 languageEnglish (US)
Pages (from-to)216-239
Number of pages24
JournalAdvances in Applied Mathematics
Volume47
Issue number2
DOIs
StatePublished - 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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