Bimahonian distributions

• Autores: Elena Barcelo, Victor Reiner
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 627-646
• Idioma: inglés
• DOI: 10.1112/jlms/jdn004
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• Resumen

  • 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.