Comparing sumsets and difference sets

  • Date: 09/19/2006

Greg Martin (University of British Columbia)


University of British Columbia


Since addition is commutative but subtraction is not, the subset S+S of
a finite set S is predisposed to be smaller than the difference set
S-S. As Mel Nathanson wrote:

Even though there exist sets S that have more sums than differences,
such sets should be rare, and it must be true with the right way of
counting that the vast majority of sets satisfy |S-S| > |S+S|.

We talk about joint work with Kevin O'Bryant in which we probe this
statement from various angles, indicating what's right and what's wrong
with Nathanson's belief.

Other Information: 

Discrete Math Seminar 2006