The combinatorics of associated Hermite polynomials

Details The combinatorics of associated Hermite polynomials The combinatorics of associated Hermite polynomials

2007-09-07

arxiv.org/abs/0709.0987v3

European J. Combinatorics, May 2009, vol 30 no 4, pp 1005-1021

Mathematics

Combinatorics

[v1]: 18 pages, 16 figures; presented at FPSAC 2007 [v2]: Some minor errors fixed (thanks Bill Chen, Jang Soo Kim) and text re

Scientific paper

10.1016/j.ejc.2008.05.009

We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and rooted maps and show weight-preserving bijections between these objects. Several identities, linearization formulas, the moment generating function, and a second combinatorial model are also derived.

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