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arXiv · 0806.3046

A Filtration of (q,t)-Catalan numbers

N. Bergeron·F. Descouens·M. Zabrocki
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Abstract

We define new generalizations of (q,t)-Catalan numbers applying nabla operator on k-Schur functions indexed by column partitions. In some special cases, we give a combinatorial interpretation of these numbers using configurations of Dyck paths. In some other special cases, we also interpret these new polynomial as Hilbert series of explicit sub-modules of the alternating diagonal harmonics built using differential operators.

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N. Bergeron, F. Descouens, M. Zabrocki. 2008-09-12. A Filtration of (q,t)-Catalan numbers. https://doi.org/10.1016/j.aam.2009.03.002

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