Papers › On the cardinality of sets in Rᵈ obeying a slightly obtuse angle bound
On the cardinality of sets in Rᵈ obeying a slightly obtuse angle bound
Tongseok Lim, Robert J. McCann
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In this paper we explicitly estimate the number of points in a subset A ⊂ᵈ as a function of the maximum angle ∠A that any three of these points form, provided ∠A < θ_d := arccos(-1/d) ∈(π/2,π). We also show ∠A < θ_d ensures that A coincides with the vertex set of a convex polytope. This study is motivated by a question of Paul Erd\H{o}s and indirectly by a conjecture of L\'aszl\'o Fejes T\'oth.
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