The combinatorics of associated Hermite polynomials

Authors:
Dan Drake
Affiliations:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
Venue:
European Journal of Combinatorics
Year:
2009

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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.