The linear forms x+y and x+2y

For any finite set of integers, let S(A) = {a+a' : a,a' in A} and let T(A) = {a+2a' : a,a' in A}. Computations of Kevin O'Bryant and Tom Morgan indicate |S(A)| < |T(A)| for small sets A. An argument of Ruzsa shows that there exist very large sets A such that |S(A)| > |T(A)|. This talk will give Ruzsa's argument and some generalizations.

Mel Nathanson