Symmetric unimodal expansions of excedances in colored permutations

  title={Symmetric unimodal expansions of excedances in colored permutations},
  author={Heesung Shin and Jiang Zeng},
  journal={Eur. J. Comb.},
We consider several generalizations of the classical γ-positivity of Eulerian polynomials using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We also prove the γ-positivity for Eulerian polynomials of type B and for Eulerian polynomials of r-colored permutations. Our results solve and generalize some recent results in the literature. 


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