Danny Scheinerman, Rutgers University

Abstract

Call a subset A of an abelian group G unique sum free (USF) if every sum s in A+A is not uniquely represented. That is, for every a and b in A there exists c and d in A with a+b=c+d and the sets {a,b} and {c,d} are different. For A in F_p we can ask how small a USF set can be. We will show a lower bound of Theta(log(p)) and an upper bound of Theta(log^2 p). Closing this gap is an open problem. We'll discuss some generalizations.