Resumen de Bimahonian distributions

Elena Barcelo, Victor Reiner

• Motivated by permutation statistics, we define, for any complex reflection group W, a family of bivariate generating functions W(t, q). 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 shown that W(t, q) satisfies a �bicyclic sieving phenomenon� which combinatorially interprets its values when t and q are certain roots of unity.