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Bisectors and pinned distances

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arxiv 1810.00765 v1 pith:FZ4M6WMR submitted 2018-10-01 math.CO

Ben Lund , Giorgis Petridis This is my paper · ORCID
classification math.CO
keywords bounddistancespinnedprovesubsetsbisectorbisectorsconditions
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We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their bisector energy.

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  1. Bisector energy and pinned distances in positive characteristic

    math.CO 2019-08 conditional novelty 6.0 of 10

    For A in F_q^2 with |A| at most p^{4/3}, some point of A determines Ω(|A|^{2/3}) distinct distances, improving the earlier Ω(|A|^{20/37}) bound.

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