A Filtration of (q,t)-Catalan numbers
Combinatorics
2016-11-08 v2
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.
Keywords
Cite
@article{arxiv.0806.3046,
title = {A Filtration of (q,t)-Catalan numbers},
author = {N. Bergeron and F. Descouens and M. Zabrocki},
journal= {arXiv preprint arXiv:0806.3046},
year = {2016}
}