No abstract

Sum-free sets and some of their applications to number theory and Ramsey theory are reported. We also outline a recent link between sum-free sets and the numbers induced by short coverings. Given a prime power q, define c(q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space differs in at most 1 coordinate from a multiple of a vector in H. We state two extremal problems aiming to discuss a known connection between the corresponding coverings and sum-free sets, which yield classes of coverings.