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.

中文翻译：

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二项式欧拉多项式用于彩色置换

二项式欧拉多项式最先出现在Postnikov，Reiner和Williams的著作中，涉及广义变位体的枚举。它们是γ阳性（特别是回文和单峰），其可被解释为多项式ħ某些标志单纯多面体的-polynomials和承认有趣的Schur γ阳性对称函数概括。本文介绍了具有类似性质的r色置换的这些多项式的类似物，并揭示了几何组合学中等变γ正性的一些新实例。