Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655364 | Journal of Combinatorial Theory, Series A | 2014 | 16 Pages |
Abstract
We study the statistics areaarea, bouncebounce and dinvdinv on the set of parallelogram polyominoes having a rectangular m times n bounding box. We show that the bi-statistics (area,bounce)(area,bounce) and (area,dinv)(area,dinv) give rise to the same q,tq,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,tq,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,tq,t-Narayana polynomials which relates them to the famous diagonal harmonics.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jean-Christophe Aval, Michele DʼAdderio, Mark Dukes, Angela Hicks, Yvan Le Borgne,