代数图基础 本书特色

     刘彥佩编著的《代数图基础》以图的代数表示为起点，着重于多面形、 曲面、嵌入和地图等对象，用一个统一的理论框架，揭示在更具普遍性的组 合乃至代数构形中，可通过局部对称性反映全局性质。特别是通过多项式型 的不变量刻画这些构形在不同拓扑、组合和代数变换下的分类。同时，也提 供这些分类在算法上的实现和复杂性分析。虽然本书中的结论多以作者的前 期工作为基...

代数图基础 内容简介

    刘彥佩编著的《代数图基础》是中国科学技术大学校友文库之一。本书以图的代数表示为起点，着重于多面形、曲面、嵌入和地图等对象，用一个统一的理论框架，揭示在更具普遍性的组合乃至代数构形中，可通过局部对称性反映全局性质。特别是通过多项式型的不变量刻画这些构形在不同拓扑、组合和代数变换下的分类。同时，也提供这些分类在算法上的实现和复杂性分析。

代数图基础 目录

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
 2．1 ground sets
 2．2 basic permutations
 2．3 conjugate axiom
 2．4 nansitive axiom
 2．5 included angles
 2．6 notes
chapter 3 duality
 3．1 dual maps
 3．2 deletion of an edge
 3．3 addition of an edge
 3．4 basic transformation
 3．5 nores
chapter 4 orientability
 4.1 orientation
 4.2 basic equivalence
 4.3 euler characteristic
 4.4 pattern examples
 4.5 notes
chapter 5 orientable maps
 5.1 butterflies
 5.2 simplified butterflies
 5.3 reduced rules
 5.4 orientable principles
 5.5 orientable genus
 5.6 notes
chapter 6 nonorientable maps
 6.1 barflies
 6.2 simplified barflies
 6.3 nonorientable rules
 6.4 nonorientable principles
 6.5 nonorientable genus
 6.6 notes
chapter 7 isomorphisms of maps
 7.1 commutativity
 7.2 isomorphism theorem
 7.3 recognition
 7.4 justification
 7.5 pattern examples
 7.6 notes
chapter 8 asymmetrization
 8.1 automorphisms
 8.2 upper bounds of group order
 8.3 determination of the group
 8.4 rootings
 8.5 notes
chapter 9 asymmetrized petal bundles
 9.1 orientable petal bundles
 9.2 planar pedal bundles 
 9.3 nonorientable pedal bundles
 9.4 the number of pedal bundles
 9.5 notes
chapter 10 asymmetrized maps
 10.1 orientable equation
 10.2 planar rooted maps
 10.3 nonorientable equation
 10.4 gross equation
 10.5 the number of rooted maps
 10.6 notes
chapter 11 maps within symmetry
 11.1 symmetric relation
 11.2 an application
 11.3 symmetric principle
 11.4 general examples
 11.5 notes
chapter 12 genus polynomials
 12.1 associate surfaces
 12.2 layer division of a surface
 12.3 handle polynomials
 12.4 crosscap polynomials
 12.5 notes
chapter 13 census with partitions
 13.1 planted trees
 13.2 hamiltonian cubic maps
 13.3 halin maps
 13.4 biboundary inner rooted maps
 13.5 general maps
 13.6 pan-flowers
 13.7 notes
chapter 14 equations with partitions
 14.1 the meson functional
 14.2 general maps on the sphere
 14.3 nonseparable maps on the sphere
 14.4 maps without cut-edge on surfaces
 14.5 eulerian maps on the sphere
 14.6 eulerian maps on surfaces
 14.7 notes
chapter 15 upper maps of a graph
 15.1 semi-automorphisms on a graph

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自然科学 数学 代数数论组合理论

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