论文标题
dessins d'Enfants的等效类别有两个顶点
Equivalence classes of dessins d'enfants with two vertices
论文作者
论文摘要
让$ n $成为一个积极的整数。对于任何积极的整数$ l \ leq n $和$ n $的任何正数$ r $ r $ r $ r $ r $，我们列举了具有$ n $边缘，$ l $ faces和两个顶点的dessins d'Enfants的等价类别，其自动形态群体是订单$ r $的循环。此外，对于任何非负整数$ h $，我们列举了具有$ n $边缘的Dessins的等效类别，$ h $ faces of Leg $ 2 $带有$ h \ leq n $的$ 2 $和两个顶点，其自动形态群体是订单$ r $的循环。我们的论点本质上是基于所有dessins的自然一对一对应关系，其$ n $边缘与所有成对排列的等价类别具有与$ n $ $ n $的对称群体的及物子组的所有排列的等价类。
Let $N$ be a positive integer. For any positive integer $L\leq N$ and any positive divisor $r$ of $N$, we enumerate the equivalence classes of dessins d'enfants with $N$ edges, $L$ faces and two vertices whose automorphism groups are cyclic of order $r$. Further, for any non-negative integer $h$, we enumerate the equivalence classes of dessins with $N$ edges, $h$ faces of degree $2$ with $h\leq N$, and two vertices, whose automorphism groups are cyclic of order $r$. Our arguments are essentially based upon a natural one-to-one correspondence of the equivalence classes of all dessins with $N$ edges to the equivalence classes of all pairs of permutations with components generating transitive subgroups of the symmetric group of degree $N$.
