The Matrix Ansatz, Orthogonal Polynomials, and Permutations

Sylvie Corteel, Matthieu Josuat-Vergès, Lauren K. Williams

Published 2010-05-15Version 1

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.