A Filtration of (q,t)-Catalan numbers
arXiv:0806.3046 · doi:10.1016/j.aam.2009.03.002
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.