论文标题
通勤欧拉运营商
Commuting Eulerian operators
论文作者
论文摘要
由Visontai和Dey-Sivasubramanian在某些多项式的伽马积极性上的工作激励，我们发现了一对欧拉（Eulerian）操作员的交换性能。作为一个应用程序，我们向下降多项式展示了多项式对多项式$ \ {1^{a_1}，2^{a_2}，\ ldots，n^{a_n} \} $的排列的排列。因此，这些下降多项式都在交替增加，因此它们在中间有模式的单峰。
Motivated by the work of Visontai and Dey-Sivasubramanian on the gamma-positivity of some polynomials, we find 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 $\{1^{a_1},2^{a_2},\ldots,n^{a_n}\}$, where $0\leqslant a_i\leqslant 2$. Therefore, these descent polynomials are all alternatingly increasing, and so they are unimodal with modes in the middle.
