Abstract
Motivated by the work of Visontai and Dey–Sivasubramanian on the gamma-positivity of some polynomials, we discover the commutative property of a pair of Eulerian operators. As an application, we show the bi-gamma-positivity of the descent polynomials on permutations of the multiset {1a1,2a2,…,nan}, where 0⩽ai⩽2. Therefore, these descent polynomials are all alternatingly increasing, and so they are unimodal with modes in the middle.
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