球面和射影平面上不可分地图的色和

给出了球面和射影平面上带根不可分地图的色和方程,从色和方程导出了球面和射影平面上带根一般不可分地图、二部地图的计数函数方程. 利用色和理论,研究不同类地图的计数问题,得到了一种研究计数问题的新方法. 此外,还得到了一些计数显示表达式.     

克莱茵瓶上奇异地图的色数

A map is singular if each edge is on the same face on a surface (i.e., it has only one face on a surface). In this paper we present the chromatic enumeration for rooted singular maps on the Klein bottle.     

平面上一般地图的色和与双色和

本文研究了平面上一般带根地图的色和与双色和,得到了这类地图的色和与双色和函数方程。从这类地图的色和函数方程,导出了平面上一般无环地图、平面上二部地图和平面上欧拉地图的计数函数方程。还得到了一些计数函数的计数显式。     

关于双奇异平面地图的计数

本文讨论了带根双奇异平面地图的计数问题,提供了以根面次、度和内面数为参数及以根面次、奇异边数和自环数为参数的计数函数所满足的计数方程,并且导出了所有的计数显式.     

关于平面树色和方程结果的一个注记

这篇文章得到了有根平面树的节点剖分的色和方程. 导出了带无限多个参数的有根平面植树和平面树的色和方程的精确表达式. 作为直接推论可推出节点剖分的有根平面树的计数方程的精确结果 .     

Klein瓶上的双奇异地图

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、手柄上本质环数和又帽上本质环数为参数的计数公式，并得到了部分计数显式。     

环面上一般有根地图的计数

这篇文章给出了环面上以内面个数，根面次和非根节点个数为参数的一般有根地图的计数方程，导出了以内面个数和非根节点个数为参数的这类地图的计数方程的精确解。作为推论，推出了以边数为参数的这类地图的个数，其近似解在文献[2]中已讨论。     

环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

Caylay射影平面的全实曲面

It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.     

射影平面上不可分近三角剖分地图的计算

众所周知,由于本质圈(或不可收缩圈)的作用,使得一般的曲面上要得到带有两到三个参数的地图计算公式(尤其是显式公式)变得十分困难。该文集中讨论射影平面上不可分近三角剖分地图的计算。通过引入含有面次,边数和内部面数的参数表达式与Lagrangian反演,作者得到了含有正项系数的显式公式用以计算射影平面上三角剖分地图 。     

Projective Bundles of Singular Plane Cubics

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard to handle, it has been shown in [Keb00] that there exists a partial resolution of singularities which transforms a bundle of possibly badly singular curves into a bundle of nodal and cuspidal plane cubics. In cases which are of interest for classification theory, the total spaces of th se bundles will clearly be projective. It is, however, generally false that an arbitrary bundle of plane cubics is globally projective. For that reason the question of projectivity and the study of moduli seems to be of interest, and the present work gives a characterization of the projective bundles.     

环面上有根欧拉地图的计数

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．     

Klein瓶上的奇异地图

It is well known that singular maps (i. e. ,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs. In this paper the number of rooted singular maps on the Klein bottle is studied. An explicit form of the enumerating function according to the root-valency and the size of the map is determined. Further ,an expression of the vertex partition function is also found.     

The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle

A graph is said to be k-extendable if any independent set of k edges extends to a perfect matching. We shall show that every 5-connected graph of even order embedded on the projective plane and every 6-connected one embedded on the torus and the Klein bottle is 2-extendable and characterize the forbidden structures for 5-connected toroidal graphs to be 2-extendable.     

Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

多重圈梯图在射影平面上的嵌入个数

图在不同亏格曲面上的嵌入个数常常有相关关系,因此,分析一些图类在小亏格曲面上的嵌入个数对最终确定图的亏格分布和完全亏格分布有着重要意义,本文利用嵌入的联树模型得出了多重圈梯图在射影平面上的嵌入个数.