论文标题
Narayana多项式和Eulerian多项式的阳性
Positivity of Narayana polynomials and Eulerian polynomials
论文作者
论文摘要
伽马积极性在有限的几何形状，组合学和数理论中经常出现。由Sagan和Tirrell最近的工作（Adv。Math。，374（2020），107387）的动机，我们研究了伽马积极性与交替的伽马积极性之间的关系。作为应用，我们得出了几种与Narayana多项式和Eulerian多项式相关的交替γ阳性多项式。特别是，我们展示了A和B型的修改后的Narayana多项式组合的交替γ-阳性和Hurwitz的稳定性。我们使用有色$ 2 \ times n $ Young图表，我们提供了三种涉及Narayana数字的统一的组合解释。涉及本文的三种形式。在本文的最后，我们提出了两种猜想，一个涉及硼摩尔多项式，而另一个涉及下降和淘汰的置换者的枚举。
Gamma-positivity appears frequently in finite geometries, combinatorics and number theory. Motivated by the recent work of Sagan and Tirrell (Adv. Math., 374 (2020), 107387), we study the relationships between gamma-positivity and alternating gamma-positivity. As applications, we derive several alternatingly gamma-positive polynomials related to Narayana polynomials and Eulerian polynomials. In particular, we show the alternating gamma-positivity and Hurwitz stability of a combination of the modified Narayana polynomials of types A and B. By using colored $2\times n$ Young diagrams, we present a unified combinatorial interpretations of three identities involving Narayana numbers of type B. A general result of this paper is that every gamma-positive polynomial is also alternatingly semi-gamma-positive. At the end of this paper, we pose two conjectures, one concerns the Boros-Moll polynomials and the other concerns the enumerators of permutations by descents and excedances.
