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Lectures on Advances in Combinatorics

Lectures on Advances in Combinatorics
Catalogue Information
Field name Details
Dewey Class 511.6
Title Lectures on Advances in Combinatorics (EB) / by Rudolf Ahlswede, Vladimir Blinovsky.
Author Ahlswede, Rudolf
Added Personal Name Blinovsky, Vladimir
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 2008.
Physical Details : online resource.
Series Universitext
ISBN 9783540786023
Summary Note The 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 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 readerâs eyes to new interconnections.:
Contents note 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 -- Appendix: Supplementary Matrial and Research Problems -- References -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-3-540-78602-3
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