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colbourn charles j. (curatore); dinitz jeffrey h. (curatore) - handbook of combinatorial designs, second edition

Handbook of Combinatorial Designs, Second Edition

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Dettagli

Genere:Libro
Lingua: Inglese
Pubblicazione: 11/2006
Edizione: Edizione nuova, 2° edizione





Trama

Continuing in the bestselling, informative tradition of the first edition, this second edition remains the only resource to contain all of the most important results and tables in the area of combinatorial design. The handbook covers the constructions of designs, existence results, properties of designs, and applications of designs. Over 30% longer than the first edition, it contains new chapters on the history of design theory, various codes, bent functions, and numerous designs as well as updated tables, including BIBDs, PBDs, MOLS, and Hadamard matrices. With expanded and updated coverage, the book features new applications in cryptography, computer science, and finance.




Note Editore

Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results.Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory.New to the Second EditionAn introductory part that provides a general overview and a historical perspective of the areaNew chapters on the history of design theory, various codes, bent functions, and numerous types of designsFully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matricesNearly 2,200 references in a single bibliographic sectionMeeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline. The author maintains a website with more information.




Sommario

PREFACEINTRODUCTIONNEW! Opening the DoorNEW! Design Theory: Antiquity to 1950BLOCK DESIGNS2-(v, k, ?) Designs of Small OrderNEW! Triple SystemsBIBDs with Small Block Sizet-Designs with t = 3Steiner SystemsSymmetric DesignsResolvable and Near-Resolvable DesignsLATIN SQUARESLatin SquaresQuasigroupsMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSSelf-Orthogonal Latin Squares (SOLS)Orthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPAIRWISE BALANCED DESIGNSPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosureNEW! Group Divisible DesignsPBDs, Frames, and ResolvabilityPairwise Balanced Designs as Linear SpacesHADAMARD MATRICES AND RELATED DESIGNSHadamard Matrices and Hadamard DesignsOrthogonal DesignsD-Optimal MatricesBhaskar Rao DesignsGeneralized Hadamard MatricesBalanced Generalized Weighing Matrices and Conference MatricesSequence CorrelationComplementary, Base and Turyn SequencesNEW! Optical Orthogonal CodesOTHER COMBINATORIAL DESIGNSAssociation SchemesBalanced Ternary DesignsBalanced Tournament DesignsNEW! Bent FunctionsNEW! Block-Transitive DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCorrelation-Immune and Resilient FunctionsCostas ArraysNEW! Covering ArraysCoveringsCycle DecompositionsDefining SetsNEW! Deletion-Correcting CodesDerandomizationDifference FamiliesDifference MatricesDifference SetsDifference Triangle SetsDirected DesignsFactorial DesignsFrequency Squares and HypercubesGeneralized QuadranglesGraph DecompositionsNEW! Graph Embeddings and DesignsGraphical DesignsNEW! GroomingHall Triple SystemsHowell DesignsNEW! Infinite DesignsLinear Spaces: Geometric AspectsLotto DesignsNEW! Low Density Parity Check CodesNEW! Magic SquaresMendelsohn DesignsNEW! Nested DesignsOptimality and Efficiency: Comparing Block DesignsOrdered Designs, Perpendicular Arrays and Permutation SetsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsNEW! Perfect Hash FamiliesNEW! Permutation Codes and ArraysNEW! Permutation PolynomialsNEW! Pooling DesignsNEW! Quasi-3 DesignsQuasi-Symmetric Designs(r, ?)-designsRoom SquaresScheduling a TournamentSecrecy and Authentication CodesSkolem and Langford SequencesSpherical DesignsStartersSuperimposed Codes and Combinatorial Group TestingNEW! Supersimple DesignsThreshold and Ramp Schemes(t,m,s)-NetsTradesNEW! Turán SystemsTuscan Squarest-Wise Balanced DesignsWhist TournamentsYouden Squares and Generalized Youden DesignsRELATED MATHEMATICSCodesFinite GeometryNEW! Divisible SemiplanesGraphs and MultigraphsFactorizations of GraphsComputational Methods in Design TheoryNEW! Linear Algebra and DesignsNumber Theory and Finite FieldsFinite Groups and DesignsNEW! Designs and MatroidsStrongly Regular GraphsNEW! Directed Strongly Regular GraphsTwo-GraphsBIBLIOGRAPHYINDEX




Autore

Charles J. Colbourn, Jeffrey H. Dinitz










Altre Informazioni

ISBN:

9781584885061

Condizione: Nuovo
Collana: Discrete Mathematics and Its Applications
Dimensioni: 10 x 7 in Ø 4.30 lb
Formato: Copertina rigida
Illustration Notes:300 b/w images and 2000 equations
Pagine Arabe: 1016


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