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Seminar Details

Unique Sum-free Sets

  • Start Date: February 13, 2019
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Danny Scheinerman - Rutgers University
  • Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
  • Presentation Type: Stand Alone Presentation
  • 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.