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MARC 21

Lectures on Advances in Combinatorics
Tag	Description
020	$a9783540786023
082	$a511.6
099	$aOnline Resource: Springer
100	$aAhlswede, Rudolf.
245	$aLectures on Advances in Combinatorics$h[Ebook]$cby Rudolf Ahlswede, Vladimir Blinovsky.
260	$aBerlin, Heidelberg$bSpringer$c2008.
300	$bonline resource.
336	$atext
338	$aonline resource
440	$aUniversitext
505	$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 -- Appendix: Supplementary Matrial and Research Problems -- References -- Index.
520	$aThe main focus of these lectures is basis extremal problems and inequalities â 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 ErdÃ¶s/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of ErdÃ¶s (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 readerâs eyes to new interconnections.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aBlinovsky, Vladimir.$eauthor.
710	$aSpringerLink (Online service)
830	$aUniversitext
856	$uhttp://dx.doi.org/10.1007/978-3-540-78602-3