地图计数通论

地图计数通论

刘彦佩, 著

出版社:科学出版社

年代:2009

定价:108.0

书籍简介:

本书除改进和简化专著《Enumerative Theory of Maps》中的结果外,主要增添如下的新结果:1,在第1章,提供此论变换计数函数的3个新的基本定理。2,在第2章,用无穷矩阵幂,导出平面树的最终结果。3,在第3章,讨论小亏格曲面上的三角化。4,在第4章,给出3-正则c-网的无和显式。5,在第5章,导出曲面上Euler地图的计数方程,提供递推公式。6,在第6章,导出曲面上不可分离地图的计数方程,提供递推公式。7,在第7章,导出曲面上无环地图的计数方程,提供递推公式。8,在第8章,导出曲面上一般地图的计数方程,提供递推公式。9,9--10,在9-10章,导出曲面上的双不可分离地图的色和与梵和所满足的方程。在第11章,讨论上圈定向地图,在曲面上以亏格为参数的计数显式。12--13,在12-13章,讨论联树以及由此导出地图与图的嵌入之间的转换。在14-15章,提供从带根到无根,和从平面到非平面的一些原理。另外,书末还附有用联树模型表示的小地图在曲面上的附表。

书籍目录:

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

内容摘要:

  Thismonographisfortheoryanditsextensionsrelatedtocensusofmapsongeneralsurfacesestablishedonthebasisofwhathasbeendoneonthesurfaceofgenuszero.Inspiteofanumberofimprovedresultswithmapsonasurfaceofgenuszeroforsurfacesofgenusnotzero,twonewtheoreticallinesviaexploitingtherelationshipbetweensupermapsandembeddingsofagraphonsurfacesandviathejointtreetechniqueareinvestigatedforavarietyoftopicssuchasthoseinthedeterminationofhandleandcrosscappolynomialsofmaps,genusdistributionofembeddings,andothersrelated.Inparticular,anappendixservesastheexhaustivecountingsupermaps(rootedandnonrooted)includingthesepolynomialswithundergraphsofsmallsizeforthereadersdigests.  SincethefirstmonographtitledEnumerativeTheoryofMapsappearedonthesubjectconsideredin1999,manyadvanceshavebeenmadebytheauthorhimselfandthosedirectedbyhimundersuchatheoreticalfoundation.  Becauseofthatbookwithmuchattentiontomapsonsurfaceofgenuszero,thismonographisinprincipleconcernedwithmapsonsurfacesofgenusnotzero.Viamaintheoreticallines,thisbookisdividedintofourpartsexceptChapter1forpreliminaries.  PartonecontainsChapters2through10.Thetheoryispresentedformapsongeneralsurfacesofgenusnotnecessarytobezero.Forthetheoryonasurfaceofgenuszeroiscomprehensivelyimprovedforinvestigatingmapsonallsurfacesofgeneranotzero.  ParttwoconsistsofonlyChapter11.Relationshipsareestablishedforbuildingupabridgebetweensupermapsandembeddingsofagraphviatheirautomorphismgroups.  PartthreeconsistsofChapters12and13.Ageneraltheoryforfindinggenusdistributionofgraphembeddings,handlepolynomialsandcrosscappolynomialsofsupermapsareconstructedonthebasisofthejointtreemethodwhichenablesustotransformaprobleminahighdimensionalspaceintoaproblemonapolygon.  Allotherchapters,i.e.,Chapters14through17,aspartfourareconcernedwithseveralaspectsofmainextensionstodistinctdirections.  Anappendixservesasatlasofsupermapsoftypicalgraphsofsmallsizeonsurfacesfortheconvenienceofreaderstochecktheirunderstanding.

书籍规格:

书籍详细信息
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9787030244352
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出版地北京出版单位科学出版社
版次1版印次1
定价(元)108.0语种英文
尺寸24装帧精装
页数印数

书籍信息归属:

地图计数通论是科学出版社于2009.出版的中图分类号为 O157 的主题关于 组合数学-英文 的书籍。