The Combinatorics of Al-Salam-Chihara $q$-Laguerre polynomials
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.3232
- arXiv:
- arXiv:0810.3232
- Bibcode:
- 2008arXiv0810.3232K
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Classical Analysis and ODEs;
- Primary 05A18;
- Secondary 05A15;
- 05A30.
- E-Print:
- 23 pages, to appear in Adv. in Appl. Math.