环面上近三角剖分地图的计数

摘要

This paper provides the functional equation and parametric expression of rooted near triangulations on the torus with the size and the valency of the root-face as two parameters, and gives an explicit formula for the number of rooted near triangulations of the root face valency one on the torus with the size as a parameter.%本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式,并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解.