Combinatorial Methods with Computer Applications (Hardcover)

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.