论文标题
本地面部分布的渐近学和完整图的面部分布
Asymptotics of local face distributions and the face distribution of the complete graph
论文作者
论文摘要
我们对图形的所有$ 2- $单元格的嵌入中的面孔数量分布感兴趣，这等同于Euler公式的分布。为了研究这种分布，我们考虑了一个顶点处的局部分布。我们在此局部面部分布上显示出渐近均匀性，该分布可容纳任何具有较大顶点度的图形。 我们使用它来研究完整图的通常面部分布。我们表明，在这种情况下，本地面部分布决定了几乎所有图表的面部分布。我们使用此结果表明，大小$ $（1-O（1））的一部分| k_n | $具有与所有排列相同的面部分布，直至奇偶校验。在此过程中，我们证明了新的角色界限和在共轭类产品上的渐近均匀性。
We are interested in the distribution of the number of faces across all the $2-$cell embeddings of a graph, which is equivalent to the distribution of genus by Euler's formula. In order to study this distribution, we consider the local distribution of faces at a single vertex. We show an asymptotic uniformity on this local face distribution which holds for any graph with large vertex degrees. We use this to study the usual face distribution of the complete graph. We show that in this case, the local face distribution determines the face distribution for almost all of the whole graph. We use this result to show that a portion of the complete graph of size $(1-o(1))|K_n|$ has the same face distribution as the set of all permutations, up to parity. Along the way, we prove new character bounds and an asymptotic uniformity on conjugacy class products.
