Combinatorial Methods with Computer Applications

Combinatorial Methods with Computer Applications

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Description

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces.Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.show more

Product details

  • Electronic book text | 664 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 287 Illustrations, black and white
  • 1584887443
  • 9781584887447

Table of contents

PREFACEINTRODUCTION TO COMBINATORICSObjectives of CombinatoricsOrdering and SelectionSome Rules of CountingCounting SelectionsPermutationsGraphsNumber-Theoretic OperationsCombinatorial DesignsSEQUENCESSequences as ListsRecurrencesPascal's RecurrenceDifferences and Partial SumsFalling PowersStirling Numbers: A PreviewOrdinary Generating FunctionsSynthesizing Generating FunctionsAsymptotic EstimatesSOLVING RECURRENCESTypes of RecurrencesFinding Generating FunctionsPartial FractionsCharacteristic RootsSimultaneous RecursionsFibonacci Number IdentitiesNonconstant CoefficientsDivide-and-Conquer RelationsEVALUATING SUMSNormalizing SummationsPerturbationSumming with Generating FunctionsFinite CalculusIteration and Partitioning of SumsInclusion-ExclusionSUBSETS AND BINOMIALSBinomial Coefficient IdentitiesBinomial Inversion OperationApplications to StatisticsThe Catalan RecurrencePARTITIONS AND PERMUTATIONSStirling Subset NumbersStirling Cycle NumbersInversions and AscentsDerangementsExponential Generating FunctionsPosets and LatticesINTEGER OPERATIONSEuclidean AlgorithmChinese Remainder TheoremPolynomial DivisibilityPrime and Composite ModuliEuler Phi-FunctionThe Mobius FunctionGRAPH FUNDAMENTALSRegular GraphsWalks and DistanceTrees and Acyclic DigraphsGraph IsomorphismGraph AutomorphismSubgraphsSpanning TreesEdge WeightsGraph OperationsGRAPH THEORY TOPICSTraversabilityPlanarityColoringAnalytic Graph TheoryDigraph ModelsNetwork FlowsTopological Graph TheoryGRAPH ENUMERATIONBurnside-Polya CountingBurnside's LemmaCounting Small Simple GraphsPartitions of IntegersCalculating a Cycle IndexGeneral Graphs and DigraphsDESIGNSLatin SquaresBlock DesignsClassical Finite GeometriesProjective PlanesAffine PlanesAPPENDIXRelations and FunctionsAlgebraic SystemsFinite Fields and Vector SpacesBIBLIOGRAPHYGeneral ReadingReferencesSOLUTIONS AND HINTSINDICESA Glossary appears at the end of each chapter.show more

Review quote

... The book is very carefully written and might be a good starting point for undergraduate students. ...-Zentralblatt MATH 1168 I recently got [this] book on combinatorics and applications to computer science, and I like it so much that I am trying to re-shape some of the discrete maths courses I teach so that I could use it. I liked particularly [the] section on asymptotics, which is much more accessible for my undergrads than Graham, Knuth, and Patashnik.-Josef Lauri, University of Maltashow more