论文标题
欧拉对和欧拉复发系统
Eulerian pairs and Eulerian recurrence systems
论文作者
论文摘要
In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including flag descent polynomials for hyperoctahedral group, flag ascent-plateau polynomials for Stirling permutations, up-down run polynomials for symmetric group and alternating run多项式多项式组。作为应用，我们得出了相关的枚举多项式的某些特性。特别是，我们发现，用于Stirling置换的上升 - 平移多项式和左上蓝岩多项式都在交替增加，因此它们在中间的模式是单峰的。
In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including flag descent polynomials for hyperoctahedral group, flag ascent-plateau polynomials for Stirling permutations, up-down run polynomials for symmetric group and alternating run polynomials for hyperoctahedral group. As applications, we derive some properties of associated enumerative polynomials. In particular, we find that both the ascent-plateau polynomials and left ascent-plateau polynomials for Stirling permutations are alternatingly increasing, and so they are unimodal with modes in the middle.
