关于4-连通三角剖分的计数  

The Enumeration of Rooted 4-Connected Triangulations

作　　者：蔡俊亮[1] 刘彦佩[2] 

机构地区：[1]北京师范大学数学系,北京100875 [2]北方交通大学数学系,北京100044

出　　处：《数学学报（中文版）》2003年第1期203-208,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10271017)

摘　　要：本文讨论4-连通极大平面地图的计数问题.从地图对偶的角度考虑,它等价 于强3-连通3-正则有根平面地图的计数问题.在此,我们获得了具有一个和两个变 量的精确计数公式.本文的结果简化并推广了文[1,2]中的相应结果.In this paper the enumeration of rooted cubic strong c-nets is studied. The explicit expressions of this kind of maps with the size and the valency of the root-face as parameters are derived. Moreover, these results are also the same as those of rooted 4-connected triangulations which are the dual maps of rooted cubic strong c-nets. Here, some of the corresponding results in [1, 2] are thus simplified or generalized properly.

关 键 词：强3-连通地图 3-正则地图 三角剖分 计数函数 参数表达式 

分 类 号：O157.5[理学—数学]