• Citer

A q, t-analogue of Narayana numbers

par Aval, Jean-Christophe;D'Adderio, Michele ;Dukes, Mark;Hicks, Angela;Le Borgne, Yvan
Référence Discrete mathematics and theoretical computer science, page (623-634)
Publication Publié, 2013

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area; bounce) and (area; 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. © 2013 Discrete Mathematics and Theoretical Computer Science (DMTCS).