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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Main Author: Jukna, Stasys
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2011, 2011
Edition:2nd ed. 2011
Series:Texts in Theoretical Computer Science. An EATCS Series
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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