环面上有根欧拉地图的计数(英文)

Enumeration of Eulerian Maps on the Torus

英文关键词:map  Eulerian map（trail）  enufunction  Lagrangian.

中文摘要:

      本文探讨了环面上有限欧拉迹的计算并且提供了一个解析表达式．在此基础上，我们给出了环面上有根欧地图的计算公式．

英文摘要:

      In this article we count the number of rooted planar Eulerian trails and present an explicit enufunction for such maps. Based on this result, we count rooted Eulerian maps on the torus in an exact way.