The Number of Rooted Essential Maps on Surfaces

作     者：Wen Zhong LIU Yan Pei LIU 

作者机构：Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 210016 P. R. China Department of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2008年第24卷第8期

页      面：1303-1312页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：NNSFC under Grant 603730308 and 10571013 

主　　题：essential map enufunction Euler formula Langrangian inversion 

摘      要：In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.