Details

Subject(s)

• Computers [Browse]
• Number theory [Browse]
• Computer science—Mathematics [Browse]
• Combinatorics [Browse]
• Computer mathematics [Browse]

Series

• Texts in Theoretical Computer Science. An EATCS Series, [More in this series]
• Texts in Theoretical Computer Science. An EATCS Series, 1862-4499 [More in this series]

Subseries of

Texts in Theoretical Computer Science. An EATCS Series

Summary note

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 combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed – the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text. This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal—Katona theorem on shadows, the Lovász—Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi—Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.

Notes

Bibliographic Level Mode of Issuance: Monograph

Bibliographic references

Includes bibliographical references (pages 393-405) and indexes.

Language note

English

Contents

• 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.

Show 29 more Contents items

ISBN

3-642-17364-0

Doi

• 10.1007/978-3-642-17364-6

Statement on language in description

Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...