Bin Han: On the gamma-positivity of binomial Eulerian polynomials for colored permutations

Abstract: The binomial Eulerian polynomials, first introduced in work of Postnikov, Reiner and Williams, are gamma-positive polynomials and can be interpreted as h-polynomials of certain flag simplicial polytopes. Recently, Athanasiadis studied analogs of these polynomials for colored permutations and proved that they can be written as the sums of two gamma-positive polynomials. In this paper, we find combinatorial interpretations of Athanasiadis' gamma-positive polynomials, which lead to an alternative proof of their gamma-positivity expansions using the method of group actions on colored permutations. As an application, we give the gamma-coefficients of the symmetric decompositions of binomial Eulerian polynomials for colored permutations, which answers a problem of Athanasiadis.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260

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