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Lectures on Advances in Combinatorics
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Catalogue Information
Nome campo
dettagli
Dewey Class
511.6
Titolo
Lectures on Advances in Combinatorics ([Ebook]) / by Rudolf Ahlswede, Vladimir Blinovsky.
Autore
Ahlswede, Rudolf
Added Personal Name
Blinovsky, Vladimir
Other name(s)
SpringerLink (Online service)
Pubblicazione
Berlin, Heidelberg : Springer , 2008.
Physical Details
: online resource.
Serie
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
Link alle Opere Legate
Riferimenti soggetto:
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Combinatorics
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Computational Complexity
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Discrete Mathematics in Computer Science
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Distribution (Probability theory)
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Mathematics
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Number Theory
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Probability theory and stochastic processes
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Authors:
Ahlswede, Rudolf
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author
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Blinovsky, Vladimir
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Corporate Authors:
SpringerLink (Online service)
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Series:
Universitext
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Classification:
511.6
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511.6 (DDC 23)
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