双奇异平面地图的数目

Number of Planar Bisingular Maps

研究了双奇异平面地图的计数问题,提供了以根点次、奇异边数和自环数为参数及仅以边数为参数的计数函数所满足的计数方程,并导出了一些计数显式及前者的参数解.

This paper studies the enumeration of bisingular planar maps, provides the enumerating equations satisfied by enumerating functions with the valency of root-vertex, the number of singular edges and loops and the number of edges of maps as parameters. Moreover, some explicit expressions are also derived and the parametric solution to the former is presented.