The Matrix Ansatz, Orthogonal Polynomials, and Permutations

Details The Matrix Ansatz, Orthogonal Polynomials, and Permutations The Matrix Ansatz, Orthogonal Polynomials, and Permutations

2010-05-15

arxiv.org/abs/1005.2696v1

Mathematics

Combinatorics

to appear in Advances in Applied Mathematics, special issue for Dennis Stanton

Scientific paper

In this paper we outline a Matrix Ansatz approach to some problems of
combinatorial enumeration. The idea is that many interesting quantities can be
expressed in terms of products of matrices, where the matrices obey certain
relations. We illustrate this approach with applications to moments of
orthogonal polynomials, permutations, signed permutations, and tableaux.

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