On distinct consecutive differences

Details On distinct consecutive differences On distinct consecutive differences

2005-03-03

arxiv.org/abs/math/0503069v1

Mathematics

Combinatorics

7 pages

Scientific paper

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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