The main focus of these lectures is basic 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 numbers beingpair wise relatively prime?’, and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality. Another important feature of the book is that several of its concepts and problems arise in response to or by rephrasing questions fromInformation Theory, Computer Science, Statistical Physics. Written by specialists of the subject High educational value because it presents some very impressive research results, that have not appeared - for the most part - in book form Some theorems are of breathtaking depth and importance INDICE: 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 Material and Research Problems.- References.- Index.
- ISBN: 978-3-540-78601-6
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 310
- Fecha Publicación: 01/06/2008
- Nº Volúmenes: 1
- Idioma: Inglés