论文标题
图形的定向属分布的性格方法：两部分单黑色vertex情况
A character approach to directed genus distribution of graphs: the bipartite single-black-vertex case
论文作者
论文摘要
考虑到欧拉（Eulerian Digraph），我们考虑其面向面向嵌入的属分布。我们证明，这种分布是两个欧拉（Eulerian Digraphs）家族的对数洞穴，因此为这些家族提供了一个积极的答案，以向Bonnington，Conder，Morton和McKenna提出的一个问题（2002）提出了一个问题。我们的证明使用实用的多项式和对称组的表示理论$ \ mathbb {s} _n $。结果还扩展到了$ \ mathbb {s} _n $中的身份的某些因素化，这些因素是某些单face星座家族的旋转系统。
Given an Eulerian digraph, we consider the genus distribution of its face-oriented embeddings. We prove that such distribution is log-concave for two families of Eulerian digraphs, thus giving a positive answer for these families to a question asked in Bonnington, Conder, Morton and McKenna (2002). Our proof uses real-rooted polynomials and the representation theory of the symmetric group $\mathbb{S}_n$. The result is also extended to some factorizations of the identity in $\mathbb{S}_n$ that are rotation systems of some families of one-face constellations.
