双奇异平面地图的数目

journal6 ›› 2008, Vol. 29 ›› Issue (2): 7-9.

双奇异平面地图的数目

(长沙大学数学与信息科学系,湖南长沙 410003)

出版日期:2008-03-25 发布日期:2012-05-25
作者简介:龙述德(1972-),男,湖南邵阳人,长沙大学数学与信息科学系讲师,主要从事组合学与图论研究.
基金资助:
国家自然科学基金资助项目(10271017)

Number of Planar Bisingular Maps

(Department of Mathematics and Information Science,Changsha University，Changsha 410003,China)

Online:2008-03-25 Published:2012-05-25

摘要/Abstract

摘要：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.

关键词： 双奇异平面地图, 计数函数, 计数方程, Lagrange反演

Abstract: 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.

Key words: bisingular map, enumerating function, enumerating equation, Lagrangian inversion

龙述德, 王郡. 双奇异平面地图的数目[J]. journal6, 2008, 29(2): 7-9.

LONG Shu-De, WANG Jun. Number of Planar Bisingular Maps[J]. journal6, 2008, 29(2): 7-9.