Extremal Combinatorics: With Applications in Computer Science

By Stasys Jukna

Book Overview

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 Lov sz 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.

• Format: Hardcover
• Language: English
• ISBN: 3642173632
• ISBN13: 9783642173639
• Release Date: September 2011
• Publisher: Springer
• Length: 412 Pages
• Weight: 1.73 lbs.
• Dimensions: 0.9" x 6.1" x 9.2"