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arXiv · 1812.00434

Binomial Eulerian polynomials for colored permutations

Christos A. Athanasiadis
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Abstract

Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and Williams on the face enumeration of generalized permutohedra. They are $γ$-positive (in particular, palindromic and unimodal) polynomials which can be interpreted as $h$-polynomials of certain flag simplicial polytopes and which admit interesting Schur $γ$-positive symmetric function generalizations. This paper introduces analogues of these polynomials for $r$-colored permutations with similar properties and uncovers some new instances of equivariant $γ$-positivity in geometric combinatorics.

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Christos A. Athanasiadis. 2020-01-23. Binomial Eulerian polynomials for colored permutations. https://arxiv.org/abs/1812.00434

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