Extremal Combinatorics
Subtitle: With Applications in Computer Science
By: by Stasys Jukna
Series: Texts in Theoretical Computer Science. An EATCS Series; Texts in Theoretical Computer Science. An EATCS Series
Publisher: Springer Berlin Heidelberg
Published: 2001
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 378
ISBN-13: 9783642085598; 9783662046500
Subjects: Computational complexity; Symbolic and mathematical Logic; Computer science; Combinatorics; Mathematics; Information theory
Description: The book is a concise, self-contained and up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called gems of the theory. A wide spectrum of most powerful combinatorial tools is presented: methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A throughout discussion of some recent applications to computer science motivates the liveliness and inherent usefulness of these methods to approach problems outside combinatorics. No special combinatorial or algebraic background is assumed. All necessary elements of linear algebra and discrete probability are introduced before their combinatorial applications. Aimed primarily as an introductory text for graduates, it provides also a compact source of modern extremal combinatorics for researchers in computer science and other fields of discrete mathematics.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.
Table of contents: title: Introduction; title: I. The Classis: Counting; title: The Pigeon-Hole Principle; title: Principle of Inclusion and Exclusion; title: Systems of Distinct Representatives; title: Colorings; title: Chains and Antichains; title: Intersecting Families; title: Covers and Transversals; title: Sunflowers; title: Density and Universality; title: Designs; title: Witness Sets; title: Isolation Lemmas; title: II. The Linear Algebra Method: Basic Method; title: The Polynomial Technique; title: Monotone Span Programs; title: III. The Probabilistic Method: Basic Tools; title: Counting Sieve; title: Lovász Sieve; title: Linearity of Expectation; title: The Deletion Method; title: Second Moment Method; title: Bounding of Large Deviations; title: Randomized Algorithms; title: Derandomization; title: The Entropy Function; title: Random Walks and Search Problems; title: IV. Fragments of Ramsey Theory: Ramsey's Theorem; title: The Hales-Jewett Theorem; title: Epilogue: What Next?- Bibliography; title: Index.