论文标题
A型和B型Coxeter组的积极元素中的登记枚举枚举者的对数concovity
Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups
论文作者
论文摘要
经典的欧拉数$ a_ {n，k} $是log-concave。令$ p_ {n，k} $和$ q_ {n，k} $是带有$ k $ excedances的偶数和奇数排列的数量。在本文中，我们表明$ p_ {n，k} $和$ q_ {n，k} $是log-concave。为此，我们介绍了强大的同步和比率偏置的概念，这些概念是由2014年Gross，Mansour，Tucker和Wang引入的同步和比率优势的概念。 我们对B型Coxeter组显示了相似的结果。我们以一些猜想来强调以下内容：尽管强的同步比对数洞穴更强，但许多有趣的序列组合家族似乎都满足了这一属性。
The classical Eulerian Numbers $A_{n,k}$ are known to be log-concave. Let $P_{n,k}$ and $Q_{n,k}$ be the number of even and odd permutations with $k$ excedances. In this paper, we show that $P_{n,k}$ and $Q_{n,k}$ are log-concave. For this, we introduce the notion of strong synchronisation and ratio-alternating which are motivated by the notion of synchronisation and ratio-dominance, introduced by Gross, Mansour, Tucker and Wang in 2014. We show similar results for Type B Coxeter Groups. We finish with some conjectures to emphasize the following: though strong synchronisation is stronger than log-concavity, many pairs of interesting combinatorial families of sequences seem to satisfy this property.
