A q,t-analogue of Narayana numbers

Jean-Christophe Aval, Michele D'Adderio, Mark Dukes, Angela Hicks, Yvan Le Borgne

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationDMTCS Proceedings
Subtitle of host publication25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Place of PublicationNancy, France
Pages623-634
Number of pages12
Publication statusPublished - 2013

Keywords

  • q, t-Narayana
  • rectangular polyominoes
  • parking functions

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    Aval, J-C., D'Adderio, M., Dukes, M., Hicks, A., & Le Borgne, Y. (2013). A q,t-analogue of Narayana numbers. In DMTCS Proceedings : 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (pp. 623-634).