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Extremal Combinatorics With Applications in Computer Science /

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combi...

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Bibliografiska uppgifter
Huvudupphovsman: Jukna, Stasys. (Författare, medförfattare, http://id.loc.gov/vocabulary/relators/aut)
Institutionell upphovsman: SpringerLink (Online service)
Materialtyp: Elektronisk E-bok
Språk:English
Publicerad: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Upplaga:2nd ed. 2011.
Serie:Texts in Theoretical Computer Science. An EATCS Series,
Ämnen:
Computers.
Number theory.
Computer science—Mathematics.
Combinatorics.
Computer mathematics.
Theory of Computation.
Number Theory.
Discrete Mathematics in Computer Science.
Computational Mathematics and Numerical Analysis.
Länkar:https://doi.org/10.1007/978-3-642-17364-6
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Innehållsförteckning:
  • Preface
  • Prolog: What this Book Is About
  • Notation
  • Counting
  • Advanced Counting
  • Probabilistic Counting
  • The Pigeonhole Principle
  • Systems of Distinct Representatives
  • Sunflowers
  • Intersecting Families
  • Chains and Antichains
  • Blocking Sets and the Duality
  • Density and Universality
  • Witness Sets and Isolation
  • Designs
  • The Basic Method
  • Orthogonality and Rank Arguments
  • Eigenvalues and Graph Expansion
  • The Polynomial Method
  • Combinatorics of Codes
  • Linearity of Expectation
  • The Lovász Sieve
  • The Deletion Method
  • The Second Moment Method
  • The Entropy Function
  • Random Walks
  • Derandomization
  • Ramseyan Theorems for Numbers
  • The Hales–Jewett Theorem
  • Applications in Communications Complexity
  • References
  • Index.

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