We prove that the enumerative polynomials of Stirling multipermutations 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 Stirling multipermutations. Besides, we also provide an alternative approach to the partial γ-positivity from the stability of certain multivariate polynomials on Stirling multipermutations. Moreover, we prove the partial γ-positivity for the enumerators of multipermutations by plateaux, descents and ascents via introducing a group action on words. Since multipermutations without any plateau are Smirnov words, our result generalizes a γ-positivity result due to Linusson, Shareshian and Wachs in this special case. Interestingly, our second action on multipermutations applies also to Stirling multipermutations and results in another combinatorial expansion for their partial γ-positivity. Finally, using a modification of our second group action and Foata's first fundamental transformation, we prove the partial γ-positivity for the enumerators of multipermutations by fixed points, excedances and drops, generalizing another result of Linusson, Shareshian and Wachs for derangements of a multiset.

我们通过高原、下降和上升的统计证明了斯特林多重排列的枚举多项式是部分γ-正的。我们对 Jacobi-Stirling 置换的结果的专业化证实了最近由 Ma、Yeh 和第二指定作者提出的部分γ 正性猜想。我们的部分γ 正性扩展以及相应γ系数的组合解释是通过上下文无关文法机器和对斯特林多重排列的组动作获得的。此外，我们还提供了部分γ的替代方法-来自某些多元多项式对斯特林多重排列的稳定性的积极性。此外，我们通过引入对单词的组动作证明了高原、下降和上升的多重排列枚举数的部分γ -正性。由于没有任何平台的多重排列是 Smirnov 词，我们的结果概括了由于 Linusson、Shareshian 和 Wachs 在这种特殊情况下的γ 正性结果。有趣的是，我们对多重排列的第二个动作也适用于斯特林多重排列，并导致它们的部分γ 正性的另一个组合扩展。最后，使用我们的第二个群作用的修改和 Foata 的第一个基本变换，我们证明了部分γ-通过不动点、超出和下降的多重排列的枚举器的正性，概括了 Linusson、Shareshian 和 Wachs 对多重集的紊乱的另一个结果。