论文标题
普通的stirling排列和部分$γ$ - 积极性的高原
Plateaux on generalized Stirling permutations and partial $γ$-positivity
论文作者
论文摘要
我们证明，通过高原，下降和上升的统计数据，列举了普遍的Stirling置换的多项式列出了多项式。我们对雅各比·斯特林（Jacobi-Sirling）排列的结果的专业化证实了由于MA，YEH和第二名作者而导致的近期部分$γ$ - 积极性的猜想。我们的部分$γ$ - 积极性的扩展以及相应的$γ$ - 系数的组合解释是通过无上下文的语法机器以及对广义stirling置换的组动作获得的。此外，我们还通过某些多元多项式的稳定性为部分$γ$阳性提供了另一种方法。
We prove that the enumerative polynomials of generalized Stirling permutations by the statistics of plateaux, descents and ascents are partial $γ$-positive. Specialization of our result to the Jacobi-Stirling permutations confirms a recent partial $γ$-positivity conjecture due to Ma, Yeh and the second named author. Our partial $γ$-positivity expansion, as well as a combinatorial interpretation for the corresponding $γ$-coefficients, are obtained via the machine of context-free grammars and a group action on generalized Stirling permutations. Besides, we also provide an alternative approach to the partial $γ$-positivity from the stability of certain multivariate polynomials.
