Bimahonian distributions

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.

Final version to appear in J. London Math. Soc

Cited by in corpus (9)

• Cyclic Sieving for Plane Partitions and Symmetry
• Skew characters and cyclic sieving
• Dihedral Sieving Phenomena
• Constructions for cyclic sieving phenomena
• Projective reflection groups
• Promotion and cyclic sieving on families of SSYT
• Specializations of colored quasisymmetric functions and Euler-Mahonian identities
• Eulerian quasisymmetric functions and cyclic sieving
• Signed arc permutations