The combinatorics of associated Hermite polynomials
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. (C) 2008 Elsevier Ltd. All rights reserved.
- Issue Date
- 2009
- Language
- English
- Article Type
- Article
- Keywords
ORTHOGONAL POLYNOMIALS; CONTINUED FRACTIONS; LAGUERRE; IDENTITIES; LINEARIZATION; MATCHINGS; FILLINGS; DIAGRAMS; BIRTH
- Citation
EUROPEAN JOURNAL OF COMBINATORICS, v.30, no.4, pp.1005 - 1021
- ISSN
- 0195-6698
- Appears in Collection
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