q,t-Fuß–Catalan numbers for finite reflection groups

@article{Stump2009qtFuCatalanNF,
  title={q,t-Fu{\ss}–Catalan numbers for finite reflection groups},
  author={Christian Stump},
  journal={Journal of Algebraic Combinatorics},
  year={2009},
  volume={32},
  pages={67-97}
}
  • Christian Stump
  • Published 12 January 2009
  • Mathematics
  • Journal of Algebraic Combinatorics
In type A, the q,t-Fuß–Catalan numbers can be defined as the bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we exhibit several conjectured algebraic and combinatorial properties of these polynomials with nonnegative integer coefficients. We prove the conjectures for the dihedral groups and for the cyclic groups. Finally, we present several ideas on how the q,t-Fu… 

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