Klein瓶上的双奇异地图

摘要

A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the Klein bottle and also we present formulae for such maps with four parameters: the number of edges, the number of planar loops, the number of essential loops on handles and the number of essential loops on crosscaps.%一个地图的每条边如果不是环就是割边(即该边的两边是同一个面的边界),则称之为双奇异地图.本文研究Klein瓶上带根双奇异地图的计数问题,得到了此类地图以边数、平面环数、手柄上本质环数和叉帽上本质环数为参数的计数公式.并得到了部分计数显式.