Partial $\gamma$-Positivity for Quasi-Stirling Permutations of Multisets
| Autor: | Yan, Sherry H. F., Huang, Yunwei, Yang, Lihong |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin, Ma and Zhang. This is accomplished by proving the partial $\gamma$-positivity of the enumerative polynomials of certain ordered labeled trees, which are in bijection with quasi-Stirling permutations of multisets. As an application, we provide an alternative proof of the partial $\gamma$-positivity of the enumerative polynomials on Stirling permutations of multisets. Comment: arXiv admin note: text overlap with arXiv:2106.04348 |
| Databáze: | arXiv |
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