A Combinatorial Derivation with Schröder Paths of a Determinant Representation of Laurent Biorthogonal Polynomials

  • Shuhei Kamioka
DOI: https://doi.org/10.37236/800

Abstract

A combinatorial proof in terms of Schröder paths and other weighted plane paths is given for a determinant representation of Laurent biorthogonal polynomials (LBPs) and that of coefficients of their three-term recurrence equation. In this process, it is clarified that Toeplitz determinants of the moments of LBPs and their minors can be evaluated by enumerating certain kinds of configurations of Schröder paths in a plane.

Published
2008-05-31
Issue
Volume 15 (2008)
Article Number
R76