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多面形理论(英文版)|报价¥50.70|图书,科学与自然,数学,数学理论,Yanpei Liu

王朝王朝水庫·作者佚名  2008-05-21
窄屏简体版  字體: |||超大  

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目录:图书,科学与自然,数学,数学理论,

品牌:Yanpei Liu

基本信息

·出版社:科学出版社

·页码:335 页码

·出版日:2008年

·ISBN:9787030208880

·条码:9787030208880

·版次:1版(英文版)

·装帧:平装

·开本:16 16

·中文:中文

内容简介

This monograph is for a unified theory of surfaces, embeddings and maps all considered as polyhedra via the joint tree modal which was initiated from the author's articles in the seventies of last century and has been basically developed in recent decades. Complete invariants for each classification are topologically, combinatorially or isomorphically extracted. A number of counting polynomials including handle and crosscap polynomials are presented. In particular, an appendix serves as the exhaustive counting super maps (rooted and nonrooted) including these polynomials with under graphs of small size for the reader's digests.

Although the book is mainly for researchers in mathematics, theoretical physics, chemistry, biology and some others related, the basic part in each chapter can also be chosen for graduates and college teachers as references.

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目录

Preface

Chapter Ⅰ Preliminaries

Ⅰ.1 Sets and mappings

Ⅰ.2 Partitions and permutations

Ⅰ.3 Group actions

Ⅰ.4 Networks

Ⅰ.5 Notes

Chapter Ⅱ Surfaces

Ⅱ.1 Polyhedra

Ⅱ.2 Elementary equⅣalence

Ⅱ.3 Polyhegons

Ⅱ.4 Orientability

Ⅱ.5 Classification

Ⅱ.6 Notes

Chapter Ⅲ Embeddings of Graphs

Ⅲ.1 Geometric consideration

Ⅲ.2 Surface closed curve axiom

Ⅲ.3 Distinction

Ⅲ.4 Joint tree model

Ⅲ.5 Combinatorial properties

Ⅲ.6 Notes

Chapter Ⅳ Mathematical Maps

Ⅳ.1 Basic permutations

Ⅳ.2 Conjugate axiom

Ⅳ.3 TransitⅣity

Ⅳ.4 Included angles

Ⅳ.5 Notes

Chapter Ⅴ Duality on Surfaces

Ⅴ.1 Dual partition of edges

Ⅴ.5 Notes

Chapter Ⅵ Invariants on Basic Class

Ⅵ.1 Orientability

Ⅵ.2 Euler characteristic

Ⅵ.3 Basic equⅣalence

Ⅵ.4 Orientable maps

Ⅵ.5 Nonorientable maps

Ⅵ.6 Notes

Chapter Ⅶ Asymmetrization

Ⅶ.1 Isomorphisms

Ⅶ.2 Recognition

Ⅶ.3 Upper bound of group order

Ⅶ.4 Determination of the group

Ⅶ.5 Rootings

Ⅶ.6 Notes

Chapter Ⅷ Asymmetrized Census

Ⅷ.1 Orientable equation

Ⅷ.2 Planar maps...

Ⅷ.3 Nonorientable equation

Ⅷ.4 Gross equation

Ⅷ.5 The number of maps

Ⅷ.6 Notes

Chapter Ⅸ Petal Bundles

Ⅸ.1 Orientable petal bundles

Ⅸ.2 Planar pedal bundles

Ⅸ.3 Nonorientable pedal bundles

Ⅸ.4 The number of pedal bundles

Ⅸ.5 Notes

Chapter Ⅹ Super Maps of Genus Zero

Chapter Ⅺ Symmetric Census

Chapter Ⅻ Cycle Oriented Maps

Chapter ⅫⅠ Census by Genus

Chapter ⅩⅣ Classic Applications

Appendix Ⅰ Embeddings and maps of Small Size Distributed by Genus

Appendix Ⅱ Orientable Forms of Surfaces and Their Nonorientable Genus Polynomials

Bibliography

Subject Index

Author Index

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