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.
|Title of host publication||DMTCS Proceedings|
|Subtitle of host publication||25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)|
|Place of Publication||Nancy, France|
|Number of pages||12|
|Publication status||Published - 2013|
- q, t-Narayana
- rectangular polyominoes
- parking functions
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).