限制下降对 Quasi-Stirling 排列多项式的局部 γ-正性  

Partial γ-Positivity for Quasi-Stirling Permutation with Restricted Descent Pair

作　　者：朱雪 黄运威 

机构地区：[1]浙江师范大学数学系,浙江 金华

出　　处：《应用数学进展》2022年第1期116-125,共10页Advances in Applied Mathematics

摘　　要：具有 γ - 正性的多项式在组合学中是一类重要的研究对象,其不仅蕴含了单峰性以及对称性,它的实根性在代数组合学中也有深远的研究意义。本文证明了仅包含 (偶,偶) - 下降对的 quasi- Stirling 排列上的一类三元多项式具有局部 γ - 正性,并给出局部 γ - 系数的组合解释,从而推广了 Eu 等人关于普通排列的相关结果。Polynomials with γ-positivity are an important research object in combinatorics. They not only contain unimodality and symmetry, but also have far-reaching research sig- nificance in algebraic combinatorics. This paper proves that a class of ternary polyno- mials that quasi-Stirling permutation only contains (even, even)-decreasing pairs has local γ-positivity, and the combined explanation of local γ-coefficient is given, thus extending the related results of Eu on ordinary permutation.

关 键 词：Quasi-Stirling 排列 限制下降对 局部 γ - 正性 

分 类 号：O29[理学—应用数学]