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On distinct consecutive differences

J. Solymosi
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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 $|A+B|\geq c|A|^{1/2}|B|$ for any finite set of numbers $B$. The bound is tight up to the constant multiplier.

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J. Solymosi. 2005-03-03. On distinct consecutive differences. https://arxiv.org/abs/math/0503069

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