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008			110831s2011 gw | s |||| 0|eng d
020			_a9783642173646 _9978-3-642-17364-6
040			_cMX-MeUAM
050		4	_aQA75.5-76.95
082	0	4	_a004.0151 _223
100	1		_aJukna, Stasys. _eauthor.
245	1	0	_aExtremal Combinatorics _h[recurso electrónico] : _bWith Applications in Computer Science / _cby Stasys Jukna.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011.
300			_aXXIV, 412 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aTexts in Theoretical Computer Science. An EATCS Series, _x1862-4499
505	0		_aPreface -- Prolog: 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.
520			_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.
650		0	_aComputer science.
650		0	_aInformation theory.
650		0	_aComputational complexity.
650		0	_aComputer science _xMathematics.
650		0	_aCombinatorics.
650		0	_aNumber theory.
650	1	4	_aComputer Science.
650	2	4	_aTheory of Computation.
650	2	4	_aNumber Theory.
650	2	4	_aDiscrete Mathematics in Computer Science.
650	2	4	_aCombinatorics.
650	2	4	_aComputational Mathematics and Numerical Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642173639
830		0	_aTexts in Theoretical Computer Science. An EATCS Series, _x1862-4499
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-17364-6
596			_a19
942			_cLIBRO_ELEC
999			_c203364 _d203364