Bimahonian distributions

Details Bimahonian distributions Bimahonian distributions

2007-03-16

arxiv.org/abs/math/0703479v2

Mathematics

Combinatorics

Final version to appear in J. London Math. Soc

Scientific paper

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.

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