Papers › A Construction for Difference Sets with Local Properties
A Construction for Difference Sets with Local Properties
Sara Fish, Ben Lund, Adam Sheffer
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We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set A of n real numbers such that |A-A|=n^(log₂ 3) and that every subset A′⊆A of size k satisfies |A′-A′|≥k^(log₂ 3). This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.
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