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- DescriptionThis book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nspecialists. 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 kwledge 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 polymial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal-Katona theorem on shadows, the Lovasz-Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for motone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovasz Local Lemma, Schoning's algorithm for 3-SAT, the Szemeredi-Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.
- Author BiographyThe author is a professor at the Goethe Universitat Frankfurt and he is also a member of the Vilnius University Institute of Mathematics and Informatics. His main fields of research are theoretical computer science and discrete mathematics, in particular complexity.
- Author(s)Stasys Jukna
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Date of Publication01/09/2011
- Series TitleTexts in Theoretical Computer Science: An EATCS Series
- Place of PublicationBerlin
- Country of PublicationGermany
- ImprintSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Content Notebiography
- Weight812 g
- Width156 mm
- Height234 mm
- Spine23 mm
- Format DetailsLaminated cover
- Edition Statement2nd ed. 2011
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