Multivariate Eulerian Polynomials and Exclusion Processes

Brändén, Petter; Leander, Madeleine; Visontai, Mirkó

doi:10.1017/s0963548316000031

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2019

2023

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Cited by 5 publications

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“…Note that a univariate real polynomial is stable if and only if it has only real roots. Several multivariate Eulerian polynomials have been shown to be stable, see [6,9,13,29,31].…”

Section: Stabilitymentioning

confidence: 99%

Plateaux on generalized Stirling permutations and partial $γ$-positivity

Lin,

Ma,

Zhang

2020

Preprint

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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.

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“…Note that a univariate real polynomial is stable if and only if it has only real roots. Several multivariate Eulerian polynomials have been shown to be stable, see [6,9,13,29,31].…”

Section: Stabilitymentioning

confidence: 99%