Mathematical analysis reveals an improved lower bound on distinct dot products in planar point sets, advancing progress on discrete geometry problems.
We are interested to bound from below the number of distinct dot products determined by a finite set of points P in the Euclidean plane. In this paper, we build on [3] to obtain the improved lower bound | { p ⋅ q : p , q ∈ P } | ≳ | P | 2 3 + 7 1425 .
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Michalis Kokkinos (2026) studied this question.
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