The Matrix Ansatz, Orthogonal Polynomials, and Permutations

Abstract

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.

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

References in corpus (5)

• Total positivity, Grassmannians, and networks
• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• The structure of alternative tableaux
• The Combinatorics of Al-Salam-Chihara $q$-Laguerre polynomials
• Combinatorics of the three-parameter PASEP partition function