设计理论

图书标准信息

• 作者 万哲先 著
• 出版社 高等教育出版社
• 出版时间 2009-07
• 版次 1
• ISBN 9787040241648
• 定价 48.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 221页
• 字数 300千字
• 正文语种 英语
• 丛书 组合数学丛书

【内容简介】

Thisbookdealswiththebasicsubjectsofdesigntheory.Itbeginswithbalancedincompleteblockdesigns，variousconstructionsofwhicharedescribedinampledetail.Inparticular，finiteprojectiveandaffineplanes,differencesetsandHadamardmatrices，astoolstoconstructbalancedincompleteblockdesigns，areincluded.Orthogonallatinsquaresarealsotreatedindetail.Zhu'ssimplerproofofthefalsityofEuler'sconjectureisincluded.Theconstructionofsomeclassesofbalancedincompleteblockdesigns，suchasSteinertriplesystemsandKirkmantriplesystems，arealsogiven.
T-designsandpartiallybalancedincompleteblockdesigns(togetherwithassociationschemes)，asgeneralizationsofbalancedincompleteblockdesigns，areincluded.SomecodingtheoryrelatedtoSteinertriplesystemsareclearlyexplained.
Thebookiswritteninalucidstyleandisalgebraicinnature.Itcanbeusedasatextorareferencebookforgraduatestudentsandresearchersincombinatoricsandappliedmathematics.Itisalsosuitableforself-study.

【目录】

Preface
1.BIBDs
1.1DefinitionandFundamentalPropertiesofBIBDs
1.2IsomorphismsandAutomorphisms
1.3ConstructionsofNewBIBDsfromOldOnes
1.4Exercises

2.SymmetricBIBDs
2.1DefinitionandFundamentalProperties
2.2Bruck-Ryser-ChowlaTheorem
2.3FiniteProjectivePlanesasSymmetricBIBDs
2.4DifferenceSetsandSymmetricBIBDs
2.5HadamardMatricesandSymmetricBIBDs
2.6DerivedandResidualBIBDs
2.7Exercises

3.ResolvableBIBDs
3.1DefinitionsandExamples
3.2FiniteAffinePlanes
3.3PropertiesofResolvableBIBDs
3.4Exercises

4.OrthogonalLatinSquares
4.1OrthogonalLatinSquares
4.2MutuallyOrthogonalLatinSquares
4.3SingularDirectProductofLatinSquares
4.4SumCompositionofLatinSquares
4.5OrthogonalArrays
4.6TransversalDesigns
4.7Exercises

5.PairwiseBalancedDesigns；GroupDivisibleDesigns
5.1PairwiseBalancedDesigns
5.2GroupDivisibleDesigns
5.3ClosednessofSomeSetsofPositiveIntegers
5.4Exercises

6.ConstructionofSomeFamiliesofBIBDs
6.1SteinerTripleSystems
6.2CyclicSteinerTripleSystems
6.3KirkmanTripleSystems
6.4TripleSystems
6.5Biplanes
6.6Exercises

7.t-Designs
7.1DefinitionandFundamentalPropertiesoft-Designs
7.2RestrictionandExtension
7.3ExtendableSBIBDsandHadamard3-Designs
7.4FiniteInversivePlanes
7.5Exercises

8.SteinerSystems
8.1SteinerSystems
8.2SomeDesignsfromHadamard2-Designsand3-Designs
8.3SteinerSystemsS(4；11，5)andS(5；12，6)
8.4BinaryCodes
8.5BinaryGolayCodesandSteinerSystemsS(4；23，7)andS(5；24,8)
8.6Exercises

9.AssociationSchemesandPBIBDs
9.1AssociationSchemes
9.2PBIBDs
9.3AssociationSchemes(Continued)
9.4Exercises
References