The combinatorics of associated Hermite polynomials

@article{Drake2009TheCO,
  title={The combinatorics of associated Hermite polynomials},
  author={Dan Drake},
  journal={Eur. J. Comb.},
  year={2009},
  volume={30},
  pages={1005-1021}
}
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