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Graduate Student Combinatorics Seminar Sponsored by DIMACS

Unique sum-free sets

Danny Scheinerman - Rutgers University

Location:  GSL
Date & time: Wednesday, 13 February 2019 at 12:15PM - 1:15PM

 
 
 
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.

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