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＜電子ブック＞
Lectures on Advances in Combinatorics / by Rudolf Ahlswede, Vladimir Blinovsky
(Universitext. ISSN:21916675)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XIV, 318 p. 3 illus : online resource
著者標目	*Ahlswede, Rudolf author Blinovsky, Vladimir author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Probabilities LCSH:Computer science LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Number theory FREE:Discrete Mathematics FREE:Probability Theory FREE:Theory of Computation FREE:Discrete Mathematics in Computer Science FREE:Number Theory
一般注記	Conventions 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 The 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 HTTP:URL=https://doi.org/10.1007/978-3-540-78602-3

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