On Cartesian Products which Determine Few Distinct Distances
نویسندگان
چکیده
منابع مشابه
Bisector Energy and Few Distinct Distances
We introduce the bisector energy of an n-point set P in R2, defined as E(P) = ∣∣{(a, b, c, d) ∈ P | a, b have the same perpendicular bisector as c, d}∣∣ . If no line or circle contains M(n) points of P, then we prove that for any ε > 0 E(P) = O ( M(n) 2 5n 12 5 +ε +M(n)n ) . We also derive the lower bound E(P) = Ω(M(n)n2), which matches our upper bound when M(n) is large. We use our upper bound...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7736