组合数学

图书标准信息

• 作者 [美]布鲁迪 著
• 出版社 机械工业出版社
• 出版时间 2009-03
• 版次 5
• ISBN 9787111265252
• 定价 49.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 605页
• 正文语种 英语
• 丛书 经典原版书库

【内容简介】

　　《组合数学（英文版）（第5版）》英文影印版由PearsonEducationAsiaLtd，授权机械工业出版社独家出版。未经出版者书面许可，不得以任何方式复制或抄袭奉巾内容。仅限于中华人民共和国境内（不包括中国香港、澳门特别行政区和中同台湾地区）销售发行。《组合数学（英文版）（第5版）》封面贴有PearsonEducation（培生教育出版集团）激光防伪标签，无标签者不得销售。Englishreprinteditioncopyright@2009byPearsonEducationAsiaLimitedandChinaMachinePress．
　　OriginalEnglishlanguagetitle：IntroductoryCombinatorics，FifthEdition（ISBN978—0—13-602040-0）byRichardA．Brualdi，Copyright@2010，2004，1999，1992，1977byPearsonEducation，lnc．Allrightsreserved．
　　Publishedbyarrangementwiththeoriginalpublisher，PearsonEducation，Inc．publishingasPrenticeHall．
　　ForsaleanddistributioninthePeople’SRepublicofChinaexclusively（exceptTaiwan，HungKongSARandMacauSAR）．

【作者简介】

　　RichardA.Brualdi，美国威斯康星大学麦迪逊分校数学系教授（现已退休）。曾任该系主任多年。他的研究方向包括组合数学、图论、线性代数和矩阵理论、编码理论等。Brualdi教授的学术活动非常丰富。担任过多种学术期刊的主编。2000年由于“在组合数学研究中所做出的杰出终身成就”而获得组合数学及其应用学会颁发的欧拉奖章。

【目录】

1WhatIsCombinatorics?
1.1Example：PerfectCoversofChessboards
1.2Example：MagicSquares
1.3Example：TheFour-CoIorProblem
1.4Example：TheProblemofthe36C)fficers
1.5Example：Shortest-RouteProblem
1.6Example：MutuallyOverlappingCircles
1.7Example：TheGameofNim
1.8Exercises

2PermutationsandCombinations
2.1FourBasicCountingPrinciples
2.2PermutationsofSets
2.3Combinations(Subsets)ofSets
2.4PermutationsofMUltisets
2.5CornblnationsofMultisets
2.6FiniteProbability
2.7Exercises

3ThePigeonholePrinciple
3.1PigeonholePrinciple：SimpleForm
3.2PigeonholePrinciple：StrongForm
3.3ATheoremofRamsey
3.4Exercises

4GeneratingPermutationsandCornbinations
4.1GeneratingPermutations
4.2InversionsinPermutations
4.3GeneratingCombinations
4.4Generatingr-Subsets
4.5PortiaIOrdersandEquivalenceRelations
4.6Exercises

5TheBinomiafCoefficients
5.1PascalsTriangle
5.2TheBinomiaITheorem
5.3UeimodalityofBinomiaICoefficients
5.4TheMultinomialTheorem
5.5NewtonsBinomialTheorem
5.6MoreonPartiallyOrderedSets
5.7Exercises

6TheInclusion-ExclusionPrincipleandApplications
6.1TheInClusion-ExclusiOnPrinciple
6.2CombinationswithRepetition
6.3Derangements+
6.4PermutationswithForbiddenPositions
6.5AnotherForbiddenPositionProblem
6.6M6biuslnverslon
6.7Exercises

7RecurrenceRelationsandGeneratingFunctions
7.1SomeNumberSequences
7.2GeneratingFunctions
7.3ExponentialGeneratingFunctions
7.4SolvingLinearHomogeneousRecurrenceRelations
7.5NonhomogeneousRecurrenceRelations
7.6AGeometryExample
7.7Exercises

8SpecialCountingSequences
8.1CatalanNumbers
8.2DifferenceSequencesandStirlingNumbers
8.3PartitionNumbers
8.4AGeometricProblem
8.5LatticePathsandSchrSderNumbers
8.6ExercisesSystemsofDistinctReDresentatives

9.1GeneraIProblemFormulation
9.2ExistenceofSDRs
9.3StableMarriages
9.4Exercises

10CombinatoriaIDesigns
10.1ModularArithmetic
10.2BlockDesigns
10.3SteinerTripleSystems
10.4LatinSquares
10.5Exercises

11fntroductiontoGraphTheory
11.1BasicProperties
11.2EulerianTrails
11.3HamiltonPathsandCycles
11.4BipartiteMultigraphs
11.5Trees
11.6TheShannonSwitchingGame
11.7MoreonTrees
11.8Exercises

12MoreonGraphTheory
12.1ChromaticNumber
12.2PlaneandPlanarGraphs
12.3AFive-ColorTheorem
12.4IndependenceNumberandCliqueNumber
12.5MatchingNumber
12.6Connectivity
12.7Exercises

13DigraphsandNetworks
13.1Digraphs
13.2Networks
13.3MatchingsinBipartiteGraphsRevisited
13.4Exercises

14PolyaCounting
14.1PermutationandSymmetryGroups
14.2BurnsidesTheorem
14.3PolasCountingFormula
14.4Exercises
AnswersandHintstoExercises