近三正则3-连通平面地图的计数

Enumeration of Rooted Nearly Cubic C-nets

本文提供了便于依根点次，边数和根面次计数近三正则３－连通有根平面地图的一个函数方程．继之得到其参数形式解，并由此通过Ｌａｇｒａｎｇｅ反演导出了它的计数显示．本文推广了［３］和［４］的结果．

This paper provides a functional equation for enumerating rooted nearly cubic c-nets with the root-vertex valency, the size and the root-face valency of the map as three parameters. The parametric expressions are also obtained. Moreover, the explicit expressions are derived by employing Lagrangian inversion with three variables.