The combinatorics of associated Hermite polynomials

Dan Drake
2009 European journal of combinatorics (Print)  
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.
doi:10.1016/j.ejc.2008.05.009 fatcat:mawcythf5rg7tjxsde7bept26m