A Filtration of (q,t)-Catalan numbers

N. Bergeron, F. Descouens, M. Zabrocki

Published 2008-06-18, updated 2008-09-12Version 2

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.