射影平面上不可分近三角剖分地图的计算

数学物理学报 ›› 2005, Vol. 25 ›› Issue (6): 839-845.

射影平面上不可分近三角剖分地图的计算

任韩, 邓默, 刘彦佩

华东师范大学数学系上海 200062 北京交通大学理学院数学系北京 100044

出版日期:2005-12-24 发布日期:2005-12-24
基金资助:
上海市重点基金项目和上海市基础研究项目(04JC14031)、国家自然科学基金(10271048、19831080)

Counting Non separable Near triangulations on |the Projective Plane

LIN Han, DENG Mo, LIU Pan-Pei

Online:2005-12-24 Published:2005-12-24
Supported by:
上海市重点基金项目和上海市基础研究项目(04JC14031)、国家自然科学基金(10271048、19831080)

摘要/Abstract

摘要：

众所周知,由于本质圈(或不可收缩圈)的作用,使得一般的曲面上要得到带有两到三个参数的地图计算公式(尤其是显式公式)变得十分困难。该文集中讨论射影平面上不可分近三角剖分地图的计算。通过引入含有面次,边数和内部面数的参数表达式与Lagrangian反演,作者得到了含有正项系数的显式公式用以计算射影平面上三角剖分地图。

关键词: (有根)地图； Lagrangian反演；生成函数

Abstract:

It is well known that any explicit generating function wi th up to two or three parameters for nonplanar maps can not be determined with easy because of difficulties in handling the essential circuits (or “noncontractible cycles” as some scholars called). In this paper the authors count rooted nonseparatable neartriangulations on the projective plane by the rootface valency, the size, and the number of inner faces and a parametric expression, by which an explicit generating function with positive coefficients can be easily deduced, is completely determined as well.

Key words: (rooted)Map； Lagrangian inversion； Generating function

中图分类号:

05C30

任韩, 邓默, 刘彦佩. 射影平面上不可分近三角剖分地图的计算[J]. 数学物理学报, 2005, 25(6): 839-845.

LIN Han, DENG Mo, LIU Pan-Pei. Counting Non separable Near triangulations on |the Projective Plane[J]. Acta mathematica scientia,Series A, 2005, 25(6): 839-845.