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
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245 0 0 |a Extremal Combinatorics  |h Elektronische Ressource  |b With Applications in Computer Science  |c by Stasys Jukna 
250 |a 2nd ed. 2011 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2011, 2011 
300 |a XXIV, 412 p  |b online resource 
505 0 |a 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 
653 |a Theory of Computation 
653 |a Number theory 
653 |a Number Theory 
653 |a Computational Mathematics and Numerical Analysis 
653 |a Computer science / Mathematics 
653 |a Information theory 
653 |a Computational complexity 
653 |a Combinatorics 
653 |a Discrete Mathematics in Computer Science 
653 |a Combinatorics 
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989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Texts in Theoretical Computer Science. An EATCS Series 
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082 0 |a 004.0151 
520 |a 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