The combinatorics of associated Hermite polynomials

  title={The combinatorics of associated Hermite polynomials},
  author={Dan Drake},
  journal={Eur. J. Comb.},
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, and a second combinatorial model are also derived. Résumé. Nous développons un modèle… CONTINUE READING