Lectures on Advances in Combinatorics
- Author
- Rudolf Ahlswede, Vladimir Blinovsky
- Publication Year
- 2008
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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.
Keywords: Mathematics and Statistics / AZ-identities / LYM-inequality / Maxima / Number theory / Prime / Antichain splitting / Combinatorics / Diametric problems / Intersection problems
