数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (2): 313-320.

• 论文 • 上一篇    

BISINGULAR MAPS ON SOME SURFACES

李赵祥,任韩,刘彦佩   

  1. Department of Mathematics, Central University for Nationalities, Beijing 100081, China Department of Mathematics, East China Normal University, Shanghai 200062, China Department of Mathematics, Northern Jiaotong University, Beijing 100044, China
  • 出版日期:2004-07-20 发布日期:2004-07-20
  • 基金资助:

    Supported by fifteenth programming of Central Uni-
    versity for Nationalities, NNSFC under Grant No.10271048 and 19831080.

BISINGULAR MAPS ON SOME SURFACES

 LI Diao-Xiang, LIN Han, LIU Pan-Pei   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    Supported by fifteenth programming of Central Uni-
    versity for Nationalities, NNSFC under Grant No.10271048 and 19831080.

摘要:

A map is bisingular if each edge is either a loop (This paper only considers
planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the
number of rooted bisingular maps on the sphere and the torus, and also presents formulae
for such maps with three parameters: the root-valency,the number of isthmus, and the
number of planar loops.

Abstract:

A map is bisingular if each edge is either a loop (This paper only considers
planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the
number of rooted bisingular maps on the sphere and the torus, and also presents formulae
for such maps with three parameters: the root-valency,the number of isthmus, and the
number of planar loops.

Key words: Bisingular map;enumerating function;Lagrangian inversion

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