有根平面地图的节点剖分计数

On the Enumeration of Rooted Planar Maps with Vertex Partition

本文试图以带一个线性泛函的方程的观点统一处理迄今为止所得到的所有类型的有根平面地图依节点剖分的计数。例如:有根平面树、冬梅地图、单圈地图、一般平面地图、不可分离平面地图、一般Euler平面地图、不可分离Euler平面地图、一般外平面地图以及不可分离外平面地图等。并且,提出了一些目前有待解决的问题。

This paper herein provides a theoretical idea of finding functional equations with a linear functional by a variety of decompositing the set of corresponding maps to treat all the results which have been obtained up to now in the enumerations of rooted plane trees, plane wintersweets, plane unicyclic maps, rooted general, nonseparable, Eulerian general, and Eulerian nonseparable planar maps, and rooted general, nonseparable outerplanar maps unificationally.