Generalized rook polynomials and orthogonal polynomials. (English) Zbl 0693.05001

Gessel, Ira M.

q-Series and partitions, Proc. Workshop, Minneapolis/MN (USA) 1988, IMA Vol. Math. Appl. 18, 159-176 (1989).

[For the entire collection see Zbl 0687.00005.]
The author shows general Laguerre and Charlier polynomials can be used in combinatorial settings. Direct combinatorial proofs of the orthogonality are given, and also combinatorial interpretations of integrals of products of these and of Hermite polynomials.

Reviewer: R.Askey

MSC:

05A05	Permutations, words, matrices
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Laguerre polynomials; rook polynomials; Charlier polynomials

Citations:

Zbl 0687.00005