03609nmm a2200373 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245010800157250001700265260006300282300003300345505076400378653002601142653001801168653001801186653005301204653003501257653002301292653002901315653001801344653004501362653001801407710003401425041001901459989003601478490005901514856007201573082001301645520157701658EB000385822EBX0100000000000000023887400000000000000.0cr|||||||||||||||||||||130626 ||| eng a97836421736461 aJukna, Stasys00aExtremal CombinatoricshElektronische RessourcebWith Applications in Computer Sciencecby Stasys Jukna a2nd ed. 2011 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2011, 2011 aXXIV, 412 pbonline resource0 aWhat 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 aTheory of Computation aNumber theory aNumber Theory aComputational Mathematics and Numerical Analysis aComputer science / Mathematics aInformation theory aComputational complexity aCombinatorics aDiscrete Mathematics in Computer Science aCombinatorics2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aTexts in Theoretical Computer Science. An EATCS Series uhttps://doi.org/10.1007/978-3-642-17364-6?nosfx=yxVerlag3Volltext0 a004.0151 aThis 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