# Number Theory Seminar April 15, 2011

TITLE: Additive Combinatorics

SPEAKER: R. Balasubramanian

DATE: April 15, 2011 at 3:30pm in Padelford C401

ABSTRACT: A subset A of an abelian group G is sum-free if the sum of any pair of elements of A lies in the complement of A.in G. A finite abelian group G is said to be of type III, if every divisor of the order of G is congruent to 1 modulo 3. When G is not of type III, the cardinality as well as a classification of the structure of sum-free subsets of the largest possible cardinality in G was known since 1967 due to the work of Diananda and Yap.

In 2005, Ben Green and Imre Ruzsa determined the cardinality of the sum-free subsets of the largest possible cardinality in type III groups and also obtained an upper bound for the number of sum-free sets. We obtained a classification of the sum-free subsets of the largest possible cardinality in type III groups and improve the upper bound for the total number of sum-free sets which was obtained by Green and Ruzsa.