On distinct consecutive differences

Abstract

We show that if $A=\{a_1<a_2<\dots <a_k\}$ is a set of real numbers such that the differences of the consecutive elements are distinct, then for and finite $B\subset \mathbb{R}$, $$|A+B|\gg |A{|}^{1/2}|B|.$$ The bound is tight up to the constant.

This paper supersedes arXiv:math/0503069