arXiv subjects

F. Descouens

Publications and source records attributed to F. Descouens.

2 recordsLinked to original sources

arXiv2008

A Filtration of (q,t)-Catalan numbers

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.

math.CO↗

arXiv2008

A non-commutative generalization of $k$-Schur functions

We introduce non-commutative analogues of $k$-Schur functions of Lapointe-Lascoux and Morse. We give an explicit formulas for the expansions of non-commutive functions with one and two parameters in terms of these new functions. These results are similar to the conjectures existing in the commutative case.

math.CO↗