[内容简介]本书论述组合地图计数以及梵和的理论。首先对所要数(shǔ)的地图集合建立合适的分解方法,在此基础上,提出函数的和信息的方程,再进行定性与定量的分析以便能求出其特解,乃至通解或者其渐近行为。本书提供了各种类型的组合地图的简洁公式,同时也提出了值得进一步研究的问题。本书适合于高等学校运筹学专业高年级教师、学生与数学研究工作者阅读。
[目次]Preface to the USTC Alumni’S Series Preface Chapter 1 Abstract Graphs
1.1 Graphs and Networks
1.2 Surfaces
1.3 Embeddings
1.4 Abstract Representation
1.5 Nores Chapter
2 Abstract Maps
3 Duality
4 Orientability
5 Orientable Maps
6 Nonorientable Maps
7 Isomorphisms of Maps
8 Asymmetrization
9 Asymmetrized Petal Bundles
10 Asymmetrized Maps
11 Maps Within Symmetry Principle
12 Genus Polynomials
13 Census with Partitions
14 Equations with Partitions
15 Upper Maps of a Graph
16 Genera of Graphs
17 Isogemial Graphs
18 Surface Embeddability
Appendix 1 Concepts of Polyhedra, Surfaces, Embeddings and Maps Appendix
2 Table of Genus Polynomials for Embeddings and Maps of Small Size Appendix
3 Atlas of Rooted and Unrooted Maps for Small Graphs Bibliography Terminology Author Index