Georgia Institute of Technology College of Sciences

What is the minimum/maximum size of a set $A$ of integers that has the property that every integer in $\{1,2,\cdots, n\}$ can be written in at least/at most $g$ ways as a difference of elements of $A$? For the first question, we show that the limit of this minimum size divided by $\sqrt{n}$ exists and is nonzero, answering a question of Kravitz. For the second question, we give an asymptotic formula for the maximum size. We also consider the same problems but in the setting of a vector space over a finite field. During the talk we will discuss open problems and connections to coding theory and graph theory. This is joint work with Eric Schmutz.