关于4-连通三角剖分的计数

The Enumeration of Rooted 4-Connected Triangulations

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.