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Discrete Mathematics & Theoretical Computer Science |
We study the statistics $\mathsf{area}$, $\mathsf{bounce}$ and $\mathsf{dinv}$ associated to polyominoes in a rectangular box $m$ times $n$. We show that the bi-statistics ($\mathsf{area}$,$\mathsf{bounce}$) and ($\mathsf{area}$,$\mathsf{dinv}$) 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.
Source : ScholeXplorer
IsRelatedTo ARXIV 1301.3035 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jcta.2014.12.003 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1301.3035
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