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Princeton University Library Catalog
Extremal Combinatorics [electronic resource] : With Applications in Computer Science / by Stasys Jukna.
2nd ed. 2011.
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
1 online resource (XXIV, 412 p.)
Texts in Theoretical Computer Science. An EATCS Series,
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Texts in Theoretical Computer Science. An EATCS Series, 1862-4499
[More in this series]
Texts in Theoretical Computer Science. An EATCS Series
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.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references (pages 393-405) and indexes.
Prolog: What this Book Is About
The Pigeonhole Principle
Systems of Distinct Representatives
Chains and Antichains
Blocking Sets and the Duality
Density and Universality
Witness Sets and Isolation
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
Ramseyan Theorems for Numbers
The Hales–Jewett Theorem
Applications in Communications Complexity
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Extremal combinatorics : with applications in computer science / Stasys Jukna.