环面上一般有根地图的计数

摘要

This paper provides the functional equation of general rooted maps with the number of inner faces, the rooted face valency and the number of non-rooted vertices as parameters on the torus, and gives an explicit expression of the enumerating function of these maps with the number of inner faces and of non-rooted vertices, then the number of these maps with the size as a parameter whose asymptotic result had been obtained in [2] is obtained as a corollary.%这篇文章给出了环面上以内面个数,根面次和非根节点个数为参数的一般有根地图的计数方程,导出了以内面个数和非根节点个数为参数的这类地图的计数方程的精确解.作为推论,推出了以边数为参数的这类地图的个数,其近似解在文献[2]中已讨论.