A combinatorial derivation with Schröder paths of a determinant representation of Laurent biorthogonal polynomials

Summary

Summary: A combinatorial proof in terms of Schr$\ddot$oder 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 Schr$\ddot$oder paths in a plane.

Mathematics Subject Classification

05A15, 42C05, 05E35