arXiv:math/0110031 Abstract

arXiv:math/0110031 [math.CO]Abstract References Reviews Resources

Cumulants, lattice paths, and orthogonal polynomials

Published 2001-10-02, updated 2002-07-03Version 2

A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants.

Comments: 11 pages, AMS LaTeX, uses pstricks; revised according to referee's suggestions, in particular cut down last section and corrected some wrong attributions

Journal: Discrete Math. 270 (2003), no. 1-3, 177--191

DOI: 10.1016/S0012-365X(02)00834-8

Categories: math.CO

Subjects: 05A15, 46L54, 11A55, 05E35

Keywords: lattice paths, formula expressing free cumulants, express hankel determinants, corresponding orthogonal polynomials, flajolets theory

Tags: journal article

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