出版社:科学出版社
年代:2008
定价:64.0
本书通过对于图在曲面上嵌入的组合结构分析,引出一个公理系统,从而导出Tutte关于地图概念的数学意义。通过在这个公理系统下的严格推导,给出数学地图的拓扑分类,进而在每一个拓扑类中继续根据对称性分为同构类。通过构造原始迹码,或对偶迹码,求得同构类的多项式型的完全不变量。通过不对称化导出Tutte的定根方式,引进根地图的同构类,并证明每一类只有一个根地图。先确定每类地图中含根地图的数目。然后,通过恢复对称性,确定无根地图的数目。
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
ChapterIIIEmbeddlngsofGraphs
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.2Generaloperation
V.3Basicoperations
V.4Quadrangulations
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
X.1Plantedtrees
X.2Outerplanargraphs
X.3Hamiltonianplanargraphs
X.4Halingraphs
X.5Notes
ChapterXISymmetricCensus
XI.1Symmetricrelation
XI.2Anapplication
XI.3Symmetricprinciple
XI.4Generalexamples
XI.5Notes
ChapterXIICycleOrientedMaps
XII.1Cycleorientation
XII.2Pan-bouquetsonsurfaces
XII.3Boundarymaps
XII.4Graphsonsurfaces
XII.5Notes
ChapterXIIICensusbyGenus
XIII.1Associatesurfaces
XIII.2Layerdivisionofasurface
XIII.3Handlepolynomials
XIII.4Crosscappolynomials
XIII.5Mapsfromembeddings
XIII.6Graphswithsamepolynomial
XIII.7Notes
ChapterXIVClassicApplications
XIV.1Convexembeddings
XIV.2Rectilinearembeddings
XIV.3Boundarythickness
XIV.4Dehndiagramonknots
XIV.5Pottsmodelsintheoreticalphysics
XIV.6Notes
AppendixIEmbeddingsandMapsofSmallSizeDistributedbyGenus
Ax.I.1Triconnectedcubicgraphs
Ax.I.2Bouquets
Ax.I.3Wheels
Ax.I.4Linkbundles
Ax.I.5Completebipartitegraphs
Ax.I.6Quadregulargraphs
AppendixIIOrientableFormsofSurfacesandTheirNon-orientableGenusPolynomials
Ax.II.1Formsoforientable2β-surfaces
Ax.II.2Nonorientablegenuspolynomials
Bibliography
SubjectIndex
AuthorIndex
Thismonographisforaunifiedtheoryofsurfaces,embeddingsandmapsallconsideredaspolyhedraviathejointtreemodalwhichwasinitiatedfromtheauthorsarticlesintheseventiesoflastcenturyandhasbeenbasicallydevelopedinrecentdecades.Completeinvariantsforeachclassificationaretopologically,combinatoriallyorisomorphicallyextracted.Anumberofcountingpolynomialsincludinghandleandcrosscappolynomialsarepresented.Inparticular,anappendixservesastheexhaustivecountingsupermaps(rootedandnonrooted)includingthesepolynomialswithundergraphsofsmallsizeforthereadersdigests.Althoughthebookismainlyforresearchersinmathematics,theoreticalphysics,chemistry,biologyandsomeothersrelated,thebasicpartineachchaptercanalsobechosenforgraduatesandcollegeteachersasreferences.
书籍详细信息 | |||
书名 | 多面形理论站内查询相似图书 | ||
9787030208880 如需购买下载《多面形理论》pdf扫描版电子书或查询更多相关信息,请直接复制isbn,搜索即可全网搜索该ISBN | |||
出版地 | 北京 | 出版单位 | 科学出版社 |
版次 | 1版 | 印次 | 1 |
定价(元) | 64.0 | 语种 | 英文 |
尺寸 | 24 | 装帧 | 平装 |
页数 | 印数 |