  Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and
Williams on the face enumeration of generalized permutohedra. They are
$\gamma$-positive (in particular, palindromic and unimodal) polynomials which
can be interpreted as $h$-polynomials of certain flag simplicial polytopes and
which admit interesting Schur $\gamma$-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 $\gamma$-positivity in geometric combinatorics.

Combinatorics