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The combinatorics of Al-Salam-Chihara \(q\)-Laguerre polynomials. (English) Zbl 1234.05035

Summary: 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.

MSC:

05A18 Partitions of sets
05A15 Exact enumeration problems, generating functions
05A30 \(q\)-calculus and related topics
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