离散几何中的研究问题
离散几何中的研究问题封面图

离散几何中的研究问题

(美) 布拉斯 (Brass,P.) 等, 编著

出版社:科学出版社

年代:2006

定价:78.0

书籍简介:

本书包含了离散几何方面超过500个开放性问题,有很多问题是第一次出版。每一章被分成了几个相互独立的节,在每节的后面都有相应的参考文献。

书籍目录:

0.DefinitionsandNotations

1.DensityProblemsforPackingsandCoverings

1.1BasicQuestionsandDefinitions

1.2TheLeastEconomicalConvexSetsforPacking

1.3TheLeastEconomicalConvexSetsforCovering

1.4HowEconomicalAretheLatticeArrangements?

1.5PackingwithSemidisks,andtheRoleofSymmetry

1.6PackingEqualCirclesintoSquares,Circles,Spheres

1.7PackingEqualCirclesorSquaresintrip

1.8TheDensestPackingofSpheres

1.9TheDensestPackingsofSpecificConvexBodies

1.10LinkingPackingandCoveringDensities

1.11SausageProblemsandCatastrophes

2.StructuralPackingandCoveringProblems

2.1DecompositionofMultiplePackingsandCoverings

2.2SolidandSaturatedPackingsandReducedCoverings

2.3StablePackingsandCoverings

2.4KissingandNeighborlyConvexBodies

2.5ThinPackingswithManyNeighbors

2.6PermeabilityandBlockingLightRays

3.PackingandCoveringwithHomotheticCopies

3.1PotatoBagProblems

3.2overingonvexBodywithItsHomotheticCopies

3.3Levi-HadwigerCoveringProblemandIllumination

3.4CoveringallbySlabs

3.5PointTrappingandImpassableLatticeArrangements

4.TilingProblems

4.1TilingthePlanewithCongruentRegions

4.2AperiodicTilingsandTilingswithFivefoldSymmetry

4.3TilingSpacewithPolytopes

5.DistanceProblems

5.1TheMaximumNumberofUnitDistancesintheP1ane

5.2TheNumberofEqualDistancesinOtherSpaces

5.3TheMinimumNumberofDistinctDistancesintheP1an

5.4TheNumberofDistinctDistancesinOtherSpaces

5.5RepeatedDistancesinPointSetsinGeneralPosition

5.6RepeatedDistancesinPointSetsinConvexPosition

5.7FrequentSmallDistancesandTouchingPairs

5.8FrequentLargeDistances

5.9ChromaticNumberofUnit—DistanceGraphs

5.10FurtherProblemsonRepeatedDistances

5.11IntegralorRationalDistances

6.ProblemsonRepeatedSubconfigurations

6.1RepeatedSimplicesandOtherPatterns

6.2RepeatedDirections,Angles,Areas

6.3EuclideanRamseyProblems.

7.IncidenceandArrangementProblems

7.1TheMaximumNumberofIncidences

7.2Sylvester—Gallai—TypeProblems

7.3LineArrangementsSpannedbyointSet8.ProblemsonPointsinGeneralPosition

8.1StructureoftheSpaceofOrderTypes

8.2ConvexPolygonsandtheErd6s—SzekeresProblem

8.3HalvingLinesandRelatedProblems

8.4ExtremalNumberofSpecialSubconfigurations

8.5OtherProblemsonPointsinGeneralPosition

9.GraphDrawingsandGeometricGraphs

9.1GraphDrawings

9.2DrawingPlanarGraphs

9.3TheCrossingNumber

9.4OtherCrossingNumbers

9.5FromThracklestoForbiddenGeometricSubgraphs

9.6FurtherTurin-TypeProblems

9.7Ramsey—TypeProblems

9.8GeometricHypergraphs

10.LatticePointProblems

10.1PackingLatticePointsinSubspaces

10.2CoveringLatticePointsbySubspaces

10.3SetsofLatticePointsAvoidingOtherRegularities

10.4VisibilityProblemsforLatticePoints

11.GeometricInequalities

11.1IsoperimetricInequalitiesforPolygonsandPolytopes

11.2Heilbronn-TypeProblems

11.3CircumscribedandInscribedConvexSets

11.4UniversalCovers

11.5ApproximationProblems

12.Index

12.1AuthorIndex

12.2SubjectIndex

内容摘要:

  本书是由LeoMoser牵头,花赞25年著成,书中包括500余个颇具吸引力的公开问题,理解其中许多问题并不需要太多的准备知识。书中的各章很大程度上内容自含,概述了离散几何,介绍了各个问题的历史细节及最重要的相关结果。本书可作为参考书,供致力数学研究,热爱美妙数学问题并不遗余力地试图加以解决的那些专业数学家和研究生查阅。

书籍规格:

书籍详细信息
书名离散几何中的研究问题站内查询相似图书
丛书名国外数学名著系列
9787030182920
如需购买下载《离散几何中的研究问题》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
版次影印本印次1
定价(元)78.0语种英文
尺寸24装帧精装
页数印数

书籍信息归属:

离散几何中的研究问题是科学出版社于2007.01出版的中图分类号为 O18 的主题关于 离散数学:几何学-研究-英文 的书籍。