The Combinatorics of Associated Laguerre Polynomials

[摘要] The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.

[关键词] associated Laguerre polynomial;moment of orthogonal polynomials;permutation tableau