On distinct consecutive differences

Abstract

We show that if $A=\{a_1,a_2,...,a_k\}$ is a monotone increasing set of numbers, and the differences of the consecutive elements are all distinct, then $|A+B|\ge c|A{|}^{1/2}|B|$ for any finite set of numbers $B$. The bound is tight up to the constant multiplier.

7 pages