Introduction to Combinatorics

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Detalles Bibliográficos
Autor principal: Erickson, Martin J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Half Title page
  • Title page
  • Copyright page
  • Dedication
  • Preface
  • Chapter 1: Basic Counting Methods
  • 1.1 The multiplication principle
  • 1.2 Permutations
  • 1.3 Combinations
  • 1.4 Binomial coefficient identities
  • 1.5 Distributions
  • 1.6 The principle of inclusion and exclusion
  • 1.7 Fibonacci numbers
  • 1.8 Linear recurrence relations
  • 1.9 Special recurrence relations
  • 1.10 Counting and number theory
  • Notes
  • Chapter 2: Generating Functions
  • 2.1 Rational generating functions
  • 2.2 Special generating functions
  • 2.3 Partition numbers
  • 2.4 Labeled and unlabeled sets
  • 2.5 Counting with symmetry
  • 2.6 Cycle indexes
  • 2.7 Pólya's theorem
  • 2.8 The number of graphs
  • 2.9 Symmetries in domain and range
  • 2.10 Asymmetric graphs
  • Notes
  • Chapter 3: The Pigeonhole Principle
  • 3.1 The principle
  • 3.2 The lattice point problem and SET®
  • 3.3 Graphs
  • 3.4 Colorings of the plane
  • 3.5 Sequences and partial orders
  • 3.6 Subsets
  • Notes
  • Chapter 4: Ramsey Theory
  • 4.1 Ramsey's theorem
  • 4.2 Generalizations of Ramsey's theorem
  • 4.3 Ramsey numbers, bounds, and asymptotics
  • 4.4 The probabilistic method
  • 4.5 Schur's theorem
  • 4.6 Van der Waerden's theorem
  • Notes
  • Chapter 5: Error-Correcting Codes
  • 5.1 Binary codes
  • 5.2 Perfect codes
  • 5.3 Hamming codes
  • 5.4 The Fano Configuration
  • Notes
  • Chapter 6: Combinatorial Designs
  • 6.1 t-designs
  • 6.2 Block designs
  • 6.3 Projective planes
  • 6.4 Latin squares
  • 6.5 MOLS and OODs
  • 6.6 Hadamard matrices
  • 6.7 The Golay code and S(5, 8, 24)
  • 6.8 Lattices and sphere packings
  • 6.9 Leech's lattice
  • Notes
  • Appendix A: Web Resources
  • Appendix B: Notation
  • Exercise Solutions
  • References
  • Index

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