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Statistics on parallelogram polyominoes and a q, t-analogue of the Narayana numbers

par Aval, Jean-Christophe;D'Adderio, Michele ;Dukes, Mark;Hicks, Angela;Le Borgne, Yvan
Référence Journal of combinatorial theory. Series A, 123, 1, page (271-286)
Publication Publié, 2014-04

Article révisé par les pairs

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Résumé :

We study the statistics area, bounce and dinv on the set of parallelogram polyominoes having a rectangular m times n bounding box. 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 the authors in [4]. We prove the main conjectures of that paper: the q, t-Narayana polynomials are symmetric in both q and t, and m and n. This is accomplished by providing a symmetric functions interpretation of the q, t-Narayana polynomials which relates them to the famous diagonal harmonics. © 2013 Elsevier Inc.