Handbook of discrete and combinatorial mathematics - Crc Press.pdf

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HANDBOOK OF DISCRETE AND COMBINATORIAL MATHEMATICS
HANDBOOK
OF
DISCRETE AND
COMBINATORIAL
UTHEMATICS
KENNETH H. ROSEN
AT&T Laboratories
Editor-in-Chief
JOHN G. MICHAELS
SUNY Brockport
Project Editor
JONATHAN L. GROSS
Columbia University
Associate Editor
JERROLD W. GROSSMAN
Oakland University
Associate Editor
DOUGLAS R SHIER
Clemson University
Associate Editor
CRC Press
Boca Raton London New York Washington, D.C.
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CONTENTS
1. FOUNDATIONS
1.1 PropositionalandPredicateLogic — Jerrold W. Grossman
1.2 SetTheory — Jerrold W. Grossman
1.3 Functions — Jerrold W. Grossman
1.4 Relations — John G. Michaels
1.5 ProofTechniques — Susanna S. Epp
1.6 AxiomaticProgramVerification — David Riley
1.7 Logic-BasedComputerProgrammingParadigms — Mukesh Dalal
2. COUNTINGMETHODS
2.1 SummaryofCountingProblems — John G. Michaels
2.2 BasicCountingTechniques — Jay Yellen
2.3 PermutationsandCombinations — Edward W. Packel
2.4 Inclusion/Exclusion — Robert G. Rieper
2.5 Partitions — George E. Andrews
2.6 Burnside/P´olyaCountingFormula — Alan C. Tucker
2.7 M¨obiusInversionCounting — Edward A. Bender
2.8 YoungTableaux — Bruce E. Sagan
3. SEQUENCES
3.1 SpecialSequences — Thomas A. Dowling and Douglas R. Shier
3.2 GeneratingFunctions — Ralph P. Grimaldi
3.3 RecurrenceRelations — Ralph P. Grimaldi
3.4 FiniteDifferences — Jay Yellen
3.5 FiniteSumsandSummation — Victor S. Miller
3.6 AsymptoticsofSequences — Edward A. Bender
3.7 MechanicalSummationProcedures — Kenneth H. Rosen
4. NUMBERTHEORY
4.1 BasicConcepts — Kenneth H. Rosen
4.2 GreatestCommonDivisors — Kenneth H. Rosen
4.3 Congruences — Kenneth H. Rosen
4.4 PrimeNumbers — Jon F. Grantham and Carl Pomerance
4.5 Factorization — Jon F. Grantham and Carl Pomerance
4.6 ArithmeticFunctions — Kenneth H. Rosen
4.7 PrimitiveRootsandQuadraticResidues — Kenneth H. Rosen
4.8 DiophantineEquations — Bart E. Goddard
4.9 DiophantineApproximation — Jeff Shalit
4.10 QuadraticFields — Kenneth H. Rosen
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2000 by CRC Press LLC
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5. ALGEBRAICSTRUCTURES — John G. Michaels
5.1 AlgebraicModels
5.2 Groups
5.3 PermutationGroups
5.4 Rings
5.5 PolynomialRings
5.6 Fields
5.7 Lattices
5.8 BooleanAlgebras
6. LINEARALGEBRA
6.1 VectorSpaces — Joel V. Brawley
6.2 LinearTransformations — Joel V. Brawley
6.3 MatrixAlgebra — Peter R. Turner
6.4 LinearSystems — Barry Peyton and Esmond Ng
6.5 Eigenanalysis — R. B. Bapat
6.6 CombinatorialMatrixTheory — R. B. Bapat
7. DISCRETEPROBABILITY
7.1 FundamentalConcepts — Joseph R. Barr
7.2 IndependenceandDependence — Joseph R. Barr 435
7.3 RandomVariables — Joseph R. Barr
7.4 DiscreteProbabilityComputations — Peter R. Turner
7.5 RandomWalks — Patrick Jaillet
7.6 SystemReliability — Douglas R. Shier
7.7 Discrete-TimeMarkovChains — Vidyadhar G. Kulkarni
7.8 QueueingTheory — Vidyadhar G. Kulkarni
7.9 Simulation — Lawrence M. Leemis
8. GRAPHTHEORY
8.1 IntroductiontoGraphs — Lowell W. Beineke
8.2 GraphModels — Jonathan L. Gross
8.3 DirectedGraphs — Stephen B. Maurer
8.4 Distance,Connectivity,Traversability — Edward R. Scheinerman
8.5 GraphInvariantsandIsomorphismTypes — Bennet Manvel
8.6 GraphandMapColoring — Arthur T. White
8.7 PlanarDrawings — Jonathan L. Gross
8.8 TopologicalGraphTheory — Jonathan L. Gross
8.9 EnumeratingGraphs — Paul K. Stockmeyer
8.10 AlgebraicGraphTheory — Michael Doob
8.11 AnalyticGraphTheory — Stefan A. Burr
8.12 Hypergraphs — Andreas Gyarfas
9. TREES
9.1 CharacterizationsandTypesofTrees — Lisa Carbone
9.2 SpanningTrees — Uri Peled
9.3 EnumeratingTrees — Paul Stockmeyer
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2000 by CRC Press LLC
10. NETWORKSANDFLOWS
10.1 MinimumSpanningTrees — J. B. Orlin and Ravindra K. Ahuja
10.2 Matchings — Douglas R. Shier
10.3 ShortestPaths — J. B. Orlin and Ravindra K. Ahuja
10.4 MaximumFlows — J. B. Orlin and Ravindra K. Ahuja
10.5 MinimumCostFlows — J. B. Orlin and Ravindra K. Ahuja
10.6 CommunicationNetworks — David Simchi-Levi and Sunil Chopra
10.7 DifficultRoutingandAssignmentProblems — Bruce L. Golden and Bharat K. Kaku
10.8 NetworkRepresentationsandDataStructures — Douglas R. Shier
11. PARTIALLYORDEREDSETS
11.1 BasicPosetConcepts — Graham Brightwell and Douglas B. West
11.2 PosetProperties — Graham Brightwell and Douglas B. West
12. COMBINATORIALDESIGNS
12.1 BlockDesigns — Charles J. Colbourn and Jeffrey H. Dinitz
12.2 SymmetricDesigns&FiniteGeometries — Charles J. Colbourn and Jeffrey H. Dinitz
12.3 LatinSquaresandOrthogonalArrays — Charles J. Colbourn and Jeffrey H. Dinitz
12.4 Matroids — James G. Oxley
13. DISCRETEANDCOMPUTATIONALGEOMETRY
13.1 ArrangementsofGeometricObjects — Ileana Streinu
13.2 SpaceFilling — Karoly Bezdek
13.3 CombinatorialGeometry — J´anos Pach
13.4 Polyhedra — Tamal K. Dey
13.5 AlgorithmsandComplexityinComputationalGeometry — Jianer Chen
13.6 GeometricDataStructuresandSearching — Dina Kravets 853
13.7 ComputationalTechniques — Nancy M. Amato
13.8 ApplicationsofGeometry — W. Randolph Franklin
14. CODINGTHEORYANDCRYPTOLOGY — Alfred J. Menezes and
Paul C. van Oorschot
14.1 CommunicationSystemsandInformationTheory
14.2 BasicsofCodingTheory
14.3 LinearCodes
14.4 BoundsforCodes
14.5 NonlinearCodes
14.6 ConvolutionalCodes
14.7 BasicsofCryptography
14.8 Symmetric-KeySystems
14.9 Public-KeySystems
15. DISCRETEOPTIMIZATION
15.1 LinearProgramming — Beth Novick
15.2 LocationTheory — S. Louis Hakimi
15.3 PackingandCovering — Sunil Chopra and David Simchi-Levi
15.4 ActivityNets — S. E. Elmaghraby
15.5 GameTheory — Michael Mesterton-Gibbons
15.6 Sperner’sLemmaandFixedPoints — Joseph R. Barr
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2000 by CRC Press LLC

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