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arXiv · 2005.06689

Plateaux on generalized Stirling permutations and partial $\gamma$-positivity

Zhicong Lin·Jun Ma·Philip B. Zhang
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Abstract

We prove that the enumerative polynomials of generalized Stirling permutations by the statistics of plateaux, descents and ascents are partial $\gamma$-positive. Specialization of our result to the Jacobi-Stirling permutations confirms a recent partial $\gamma$-positivity conjecture due to Ma, Yeh and the second named author. Our partial $\gamma$-positivity expansion, as well as a combinatorial interpretation for the corresponding $\gamma$-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 $\gamma$-positivity from the stability of certain multivariate polynomials.

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Zhicong Lin, Jun Ma, Philip B. Zhang. 2020-05-14. Plateaux on generalized Stirling permutations and partial $\gamma$-positivity. https://arxiv.org/abs/2005.06689

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