Article ID Journal Published Year Pages File Type
4655364 Journal of Combinatorial Theory, Series A 2014 16 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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