地图计数通论（英文版）
出版时间:
2009-01
版次:
1
ISBN:
9787030244352
定价:
98.00
装帧:
精装
开本:
16开
纸张:
胶版纸
页数:
479页
正文语种:
英语
-
SincethefirstmonographtitledEnumerativeTheoryofMapsappearedonthesubjectconsideredin1999，manyadvanceshavebeenmadebytheauthorhimselfandthosedirectedbyhimundersuchatheoreticalfoundation.
Becauseofthatbookwithmuchattentiontomapsonsurfaceofgenuszero，thismonographisinprincipleconcernedwithmapsonsurfacesofgenusnotzero.Viamaintheoreticallines，thisbookisdividedintofourpartsexceptChapter1forpreliminaries.
PartonecontainsChapters2through10.Thetheoryispresentedformapsongeneralsurfacesofgenusnotnecessarytobezero.Forthetheoryonasurfaceofgenuszeroiscomprehensivelyimprovedforinvestigatingmapsonallsurfacesofgeneranotzero.
ParttwoconsistsofonlyChapter11.Relationshipsareestablishedforbuildingupabridgebetweensupermapsandembeddingsofagraphviatheirautomorphismgroups.
PartthreeconsistsofChapters12and13.Ageneraltheoryforfindinggenusdistributionofgraphembeddings，handlepolynomialsandcrosscappolynomialsofsupermapsareconstructedonthebasisofthejointtreemethodwhichenablesustotransformaprobleminahighdimensionalspaceintoaproblemonapolygon.
Allotherchapters，i.e.，Chapters14through17，aspartfourareconcernedwithseveralaspectsofmainextensionstodistinctdirections.
Anappendixservesasatlasofsupermapsoftypicalgraphsofsmallsizeonsurfacesfortheconvenienceofreaderstochecktheirunderstanding. Preface
Chapter1Preliminaries
§1.1Maps
§1.2Polynomialsonmaps
§1.3Enufunctions
§1.4Polysumfunctions
§1.5TheLagrangianinversion
§1.6Theshadowfunctional
§1.7Asymptoticestimation
§1.8Notes
Chapter2OuterplanarMaps
§2.1Planetrees
§2.2Wintersweets
§2.3Unicyclicmaps
§2.4Generalouterplanarmaps
§2.5Notes
Chapter3Triangulations
§3.1Outerplanartriangulations
§3.2Planartriangulations
§3.3Triangulationsonthedisc
§3.4Triangulationsontheprojectiveplane
§3.5Triangulationsonthetorus
§3.6Notes
Chapter4Quadrangulations
§4.1Outerplanarquadrangulations
§4.2Outerplanarquadrangulationsonthedisc
§4.3Hamiltonianquadrangulationsonthesphere
§4.4Innerendlessplanarquadrangulations
§4.5Quadrangulationsontheprojectiveplane
§4.6QuadrangulationsontheKleinbottle
§4.7Notes
Chapter5EulerianMaps
§5.1PlanarEulerianmaps
§5.2Tutteformula
§5.3Eulerianplanartriangulations
§5.4RegularEulerianplanarmaps
§5.5Eulerianmapsonsurfaces
§5.6Notes
Chapter6NonseparableMaps
§6.1Outerplanarnonseparablemaps
§6.2Euleriannonseparablemaps
§6.3Planarnonseparablemaps
§6.4Nonseparablemapsonsurfaces
§6.5Bridgelessmapsonsurfaces
§6.6Notes
Chapter7SimpleMaps
§7.1Looplessmaps
§7.2Generalsimplemaps
§7.3Simplebipartitemaps
§7.4Looplessmapsonsurfaces
§7.5Notes
Chapter8GeneralMaps
§8.1Generalplanarmaps
§8.2Planarc-nets
§8.3Convexpolyhedra
§8.4Quadrangulationsviac-nets
§8.5Generalmapsonsurfaces
§8.6Notes
Chapter9ChrosumEquations
§9.1Treeequations
§9.2Outerplanarequations
§9.3Generalequations
§9.4Triangulationequations
§9.5Welldefinedness
§9.6Chrosumsonsurfaces
§9.7Notes
Chapter10PolysumEquations
§10.1Polysumsforbitrees
§10.2Outerplanarpolysums
§10.3Generalpolysums
§10.4Nonseparablepolysums
§10.5Polysumsonsurfaces
§10.6Notes
Chapter11MapsviaEmbeddings
§11.1Automorphismgroupofagraph
§11.2Embeddingsofagraph
§11.3Supermapsofagraph
§11.4Mapsfromembeddings
§11.5Notes
Chapter12LocallyOrientedMaps
§12.1PlanarHamiltonianmaps
§12.2Biboundaryinnerrootedmaps
§12.3Boundarymaps
§12.4Cubicboundarymaps
§12.5Notes
Chapter13GenusPolynomialsofGraphs
§13.1Jointtreemodel
§13.2Layerdivisions
§13.3Graphsfromsmaller
§13.4Pan-bouquets
§13.5Notes
Chapter14FromRootedtoUnrooted
§14.1Symmetricrelations
§14.2Anapplication
§14.3Symmetricprinciples
§14.4Generalexamples
§14.5Fromundergraphs
§14.6Notes
Chapter15FromPlanartoNonplanar
§15.1Treeswithboundary
§15.2Cuttingalongvertices
§15.3Cuttingalongfaces
§15.4Mapswithaplanebase
§15.5Vertexpartition
§15.6Notes
Chapter16ChromaticSolutions
§16.1Generalsolution
§16.2Cubictriangles
§16.3Invariants
§16.4Fourcolorsolutions
§16.5Notes
Chapter17StochasticBehaviors
§17.1Asymptoticsforouterplanarmaps
§17.2Theaverageontree-rootedmaps
§17.3Hamiltoniancircuitspermap
§17.4Theasymmetryonmaps
§17.5Asymptoticsviaequations
§17.6Notes
AppendixAtlasofSuperMapsforSmallGraphs
Ax.1BouquetsBm，4≥m≥1
Ax.2LinkbundlesLm，6≥m≥3
Ax.3CompletebipartitegraphsKm，n，4≥m，n≥3
Ax.4WheelsWn，5≥n≥4
Ax.5Triconnectedcubicgraphsofsizein[6，15]
Bibliography
SubjectIndex
AuthorIndex
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内容简介:
SincethefirstmonographtitledEnumerativeTheoryofMapsappearedonthesubjectconsideredin1999，manyadvanceshavebeenmadebytheauthorhimselfandthosedirectedbyhimundersuchatheoreticalfoundation.
Becauseofthatbookwithmuchattentiontomapsonsurfaceofgenuszero，thismonographisinprincipleconcernedwithmapsonsurfacesofgenusnotzero.Viamaintheoreticallines，thisbookisdividedintofourpartsexceptChapter1forpreliminaries.
PartonecontainsChapters2through10.Thetheoryispresentedformapsongeneralsurfacesofgenusnotnecessarytobezero.Forthetheoryonasurfaceofgenuszeroiscomprehensivelyimprovedforinvestigatingmapsonallsurfacesofgeneranotzero.
ParttwoconsistsofonlyChapter11.Relationshipsareestablishedforbuildingupabridgebetweensupermapsandembeddingsofagraphviatheirautomorphismgroups.
PartthreeconsistsofChapters12and13.Ageneraltheoryforfindinggenusdistributionofgraphembeddings，handlepolynomialsandcrosscappolynomialsofsupermapsareconstructedonthebasisofthejointtreemethodwhichenablesustotransformaprobleminahighdimensionalspaceintoaproblemonapolygon.
Allotherchapters，i.e.，Chapters14through17，aspartfourareconcernedwithseveralaspectsofmainextensionstodistinctdirections.
Anappendixservesasatlasofsupermapsoftypicalgraphsofsmallsizeonsurfacesfortheconvenienceofreaderstochecktheirunderstanding.
-
目录:
Preface
Chapter1Preliminaries
§1.1Maps
§1.2Polynomialsonmaps
§1.3Enufunctions
§1.4Polysumfunctions
§1.5TheLagrangianinversion
§1.6Theshadowfunctional
§1.7Asymptoticestimation
§1.8Notes
Chapter2OuterplanarMaps
§2.1Planetrees
§2.2Wintersweets
§2.3Unicyclicmaps
§2.4Generalouterplanarmaps
§2.5Notes
Chapter3Triangulations
§3.1Outerplanartriangulations
§3.2Planartriangulations
§3.3Triangulationsonthedisc
§3.4Triangulationsontheprojectiveplane
§3.5Triangulationsonthetorus
§3.6Notes
Chapter4Quadrangulations
§4.1Outerplanarquadrangulations
§4.2Outerplanarquadrangulationsonthedisc
§4.3Hamiltonianquadrangulationsonthesphere
§4.4Innerendlessplanarquadrangulations
§4.5Quadrangulationsontheprojectiveplane
§4.6QuadrangulationsontheKleinbottle
§4.7Notes
Chapter5EulerianMaps
§5.1PlanarEulerianmaps
§5.2Tutteformula
§5.3Eulerianplanartriangulations
§5.4RegularEulerianplanarmaps
§5.5Eulerianmapsonsurfaces
§5.6Notes
Chapter6NonseparableMaps
§6.1Outerplanarnonseparablemaps
§6.2Euleriannonseparablemaps
§6.3Planarnonseparablemaps
§6.4Nonseparablemapsonsurfaces
§6.5Bridgelessmapsonsurfaces
§6.6Notes
Chapter7SimpleMaps
§7.1Looplessmaps
§7.2Generalsimplemaps
§7.3Simplebipartitemaps
§7.4Looplessmapsonsurfaces
§7.5Notes
Chapter8GeneralMaps
§8.1Generalplanarmaps
§8.2Planarc-nets
§8.3Convexpolyhedra
§8.4Quadrangulationsviac-nets
§8.5Generalmapsonsurfaces
§8.6Notes
Chapter9ChrosumEquations
§9.1Treeequations
§9.2Outerplanarequations
§9.3Generalequations
§9.4Triangulationequations
§9.5Welldefinedness
§9.6Chrosumsonsurfaces
§9.7Notes
Chapter10PolysumEquations
§10.1Polysumsforbitrees
§10.2Outerplanarpolysums
§10.3Generalpolysums
§10.4Nonseparablepolysums
§10.5Polysumsonsurfaces
§10.6Notes
Chapter11MapsviaEmbeddings
§11.1Automorphismgroupofagraph
§11.2Embeddingsofagraph
§11.3Supermapsofagraph
§11.4Mapsfromembeddings
§11.5Notes
Chapter12LocallyOrientedMaps
§12.1PlanarHamiltonianmaps
§12.2Biboundaryinnerrootedmaps
§12.3Boundarymaps
§12.4Cubicboundarymaps
§12.5Notes
Chapter13GenusPolynomialsofGraphs
§13.1Jointtreemodel
§13.2Layerdivisions
§13.3Graphsfromsmaller
§13.4Pan-bouquets
§13.5Notes
Chapter14FromRootedtoUnrooted
§14.1Symmetricrelations
§14.2Anapplication
§14.3Symmetricprinciples
§14.4Generalexamples
§14.5Fromundergraphs
§14.6Notes
Chapter15FromPlanartoNonplanar
§15.1Treeswithboundary
§15.2Cuttingalongvertices
§15.3Cuttingalongfaces
§15.4Mapswithaplanebase
§15.5Vertexpartition
§15.6Notes
Chapter16ChromaticSolutions
§16.1Generalsolution
§16.2Cubictriangles
§16.3Invariants
§16.4Fourcolorsolutions
§16.5Notes
Chapter17StochasticBehaviors
§17.1Asymptoticsforouterplanarmaps
§17.2Theaverageontree-rootedmaps
§17.3Hamiltoniancircuitspermap
§17.4Theasymmetryonmaps
§17.5Asymptoticsviaequations
§17.6Notes
AppendixAtlasofSuperMapsforSmallGraphs
Ax.1BouquetsBm，4≥m≥1
Ax.2LinkbundlesLm，6≥m≥3
Ax.3CompletebipartitegraphsKm，n，4≥m，n≥3
Ax.4WheelsWn，5≥n≥4
Ax.5Triconnectedcubicgraphsofsizein[6，15]
Bibliography
SubjectIndex
AuthorIndex
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