Article ID Journal Published Year Pages File Type
4654370 European Journal of Combinatorics 2009 17 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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