000			03298nam a22005655i 4500
001			978-3-540-78602-3
003			DE-He213
005			20161121231215.0
007			cr nn 008mamaa
008			100301s2008 gw | s |||| 0|eng d
020			_a9783540786023 _9978-3-540-78602-3
024	7		_a10.1007/978-3-540-78602-3 _2doi
050		4	_aQA150-272
072		7	_aPBD _2bicssc
072		7	_aMAT008000 _2bisacsh
082	0	4	_a511.1 _223
100	1		_aAhlswede, Rudolf. _eauthor.
245	1	0	_aLectures on Advances in Combinatorics _h[electronic resource] / _cby Rudolf Ahlswede, Vladimir Blinovsky.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008.
300			_aXIV, 318 p. 3 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aConventions and Auxiliary Results -- Intersection and Diametric Problems -- Covering, Packing, and List Codes -- Higher Level and Dimension Constrained Extremal Problems -- LYM-Related AZ-Identities, Antichain Splittings and Correlation Inequalities -- Basic Problems from Combinatorial Number Theory.
520			_aThe main focus of these lectures is basis extremal problems and inequalities – two sides of the same coin. Additionally they prepare well for approaches and methods useful and applicable in a broader mathematical context. Highlights of the book include a solution to the famous 4m-conjecture of Erdös/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of Erdös (1962) in combinatorial number theory "What is the maximal cardinality of a set of numbers smaller than n with no k+1 of its members pair wise relatively prime?", and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality. Several concepts and problems in the book arise in response to or by rephrasing questions from information theory, computer science, statistical physics. The interdisciplinary character creates an atmosphere rich of incentives for new discoveries and lends Ars Combinatoria a special status in mathematics. At the end of each chapter, problems are presented in addition to exercises and sometimes conjectures that can open a reader’s eyes to new interconnections.
650		0	_aMathematics.
650		0	_aComputers.
650		0	_aComputer science _xMathematics.
650		0	_aNumber theory.
650		0	_aProbabilities.
650		0	_aDiscrete mathematics.
650		0	_aCombinatorics.
650	1	4	_aMathematics.
650	2	4	_aDiscrete Mathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aTheory of Computation.
650	2	4	_aCombinatorics.
650	2	4	_aDiscrete Mathematics in Computer Science.
650	2	4	_aNumber Theory.
700	1		_aBlinovsky, Vladimir. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540786016
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-78602-3
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c510134 _d510134