A $q,t-$analogue of Narayana numbers - Inria - Institut national de recherche en sciences et technologies du numérique
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2013

A $q,t-$analogue of Narayana numbers

Résumé

We study the statistics $\mathsf{area}$, $\mathsf{bounce}$ and $\mathsf{dinv}$ associated to polyominoes in a rectangular box $m$ times $n$. We show that the bi-statistics ($\mathsf{area}$,$\mathsf{bounce}$) and ($\mathsf{area}$,$\mathsf{dinv}$) give rise to the same $q,t-$analogue of Narayana numbers, which was introduced by two of these authors in a recent paper. We prove the main conjectures of that same work, i.e. the symmetries in $q$ and $t$, and in $m$ and $n$ of these polynomials, by providing a symmetric functions interpretation which relates them to the famous diagonal harmonics.
Fichier principal
Vignette du fichier
dmAS0153.pdf (329.11 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01229669 , version 1 (17-11-2015)

Identifiants

Citer

Jean-Christophe Aval, Michele d'Adderio, Mark Dukes, Angela Hicks, Yvan Le Borgne. A $q,t-$analogue of Narayana numbers. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.623-634, ⟨10.46298/dmtcs.2329⟩. ⟨hal-01229669⟩
149 Consultations
838 Téléchargements

Altmetric

Partager

More