Moments of orthogonal polynomials and combinatorics

Abstract

This paper is a survey on combinatorics of moments of orthogonal polynomials and linearization coecients. This area was started by the seminal work of Flajolet followed by Viennot at the beginning of the 1980's. Over the last 30 years, several tools were conceived to extract the combinatorics and compute these moments. A survey of these techniques is presented, with applications to polynomials in the Askey scheme.