多面形理论（英文版）

图书标准信息

• 作者 Yanpei Liu 著
• 出版社 科学出版社
• 出版时间 2008-01
• 版次 1
• ISBN 9787030208880
• 定价 64.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 335页
• 正文语种 英语

【内容简介】

Thismonographisforaunifiedtheoryofsurfaces，embeddingsandmapsallconsideredaspolyhedraviathejointtreemodalwhichwasinitiatedfromtheauthorsarticlesintheseventiesoflastcenturyandhasbeenbasicallydevelopedinrecentdecades.Completeinvariantsforeachclassificationaretopologically，combinatoriallyorisomorphicallyextracted.Anumberofcountingpolynomialsincludinghandleandcrosscappolynomialsarepresented.Inparticular，anappendixservesastheexhaustivecountingsupermaps（rootedandnonrooted）includingthesepolynomialswithundergraphsofsmallsizeforthereadersdigests.
Althoughthebookismainlyforresearchersinmathematics，theoreticalphysics，chemistry，biologyandsomeothersrelated，thebasicpartineachchaptercanalsobechosenforgraduatesandcollegeteachersasreferences.

【目录】

Preface
ChapterⅠPreliminaries
Ⅰ.1Setsandmappings
Ⅰ.2Partitionsandpermutations
Ⅰ.3Groupactions
Ⅰ.4Networks
Ⅰ.5Notes

ChapterⅡSurfaces
Ⅱ.1Polyhedra
Ⅱ.2ElementaryequⅣalence
Ⅱ.3Polyhegons
Ⅱ.4Orientability
Ⅱ.5Classification
Ⅱ.6Notes

ChapterⅢEmbeddingsofGraphs
Ⅲ.1Geometricconsideration
Ⅲ.2Surfaceclosedcurveaxiom
Ⅲ.3Distinction
Ⅲ.4Jointtreemodel
Ⅲ.5Combinatorialproperties
Ⅲ.6Notes

ChapterⅣMathematicalMaps
Ⅳ.1Basicpermutations
Ⅳ.2Conjugateaxiom
Ⅳ.3TransitⅣity
Ⅳ.4Includedangles
Ⅳ.5Notes

ChapterⅤDualityonSurfaces
Ⅴ.1Dualpartitionofedges
Ⅴ.5Notes

ChapterⅥInvariantsonBasicClass
Ⅵ.1Orientability
Ⅵ.2Eulercharacteristic
Ⅵ.3BasicequⅣalence
Ⅵ.4Orientablemaps
Ⅵ.5Nonorientablemaps
Ⅵ.6Notes

ChapterⅦAsymmetrization
Ⅶ.1Isomorphisms
Ⅶ.2Recognition
Ⅶ.3Upperboundofgrouporder
Ⅶ.4Determinationofthegroup
Ⅶ.5Rootings
Ⅶ.6Notes

ChapterⅧAsymmetrizedCensus
Ⅷ.1Orientableequation
Ⅷ.2Planarmaps...
Ⅷ.3Nonorientableequation
Ⅷ.4Grossequation
Ⅷ.5Thenumberofmaps
Ⅷ.6Notes

ChapterⅨPetalBundles
Ⅸ.1Orientablepetalbundles
Ⅸ.2Planarpedalbundles
Ⅸ.3Nonorientablepedalbundles
Ⅸ.4Thenumberofpedalbundles
Ⅸ.5Notes
ChapterⅩSuperMapsofGenusZero
ChapterⅪSymmetricCensus
ChapterⅫCycleOrientedMaps
ChapterⅫⅠCensusbyGenus
ChapterⅩⅣClassicApplications
AppendixⅠEmbeddingsandmapsofSmallSizeDistributedbyGenus
AppendixⅡOrientableFormsofSurfacesandTheirNonorientableGenusPolynomials
Bibliography
SubjectIndex
AuthorIndex