Bimahonian distributions
Combinatorics
2014-02-26 v2
Abstract
Motivated by permutation statistics, we define for any complex reflection group W a family of bivariate generating functions. They are defined either in terms of Hilbert series for W-invariant polynomials when W acts diagonally on two sets of variables, or equivalently, as sums involving the fake degrees of irreducible representations for W. It is also shown that they satisfy a ``bicyclic sieving phenomenon'', which combinatorially interprets their values when the two variables are set equal to certain roots of unity.
Cite
@article{arxiv.math/0703479,
title = {Bimahonian distributions},
author = {Helene Barcelo and Victor Reiner and Dennis Stanton},
journal= {arXiv preprint arXiv:math/0703479},
year = {2014}
}
Comments
Final version to appear in J. London Math. Soc