Erdős problem 503 · problems.science

What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$ , $y$ , $z$ from $A$ , at least two of the distances $|x - y|$ , $|y - z|$ , $|x - z|$ are equal.

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

503.lean

Retained formal statement5 of 5

The best upper bound known in general is due to Blokhius [Bl84] who showed that $|A| \leq \binom{n + 2}{2}$

[Bl84] Blokhuis, A., Few-distance sets. (1984), iv+70.

FormalConjectures/ErdosProblems/503.leanErdos503.erdos_503.variants.upper_bound1 lineExact file

1∀ (n m : ℕ), m ∈ {x | ∃ A, ∃ (_ : A.IsIsosceles), A.ncard = x} → m ≤ (n + 2).choose 2

SolvedStatement only, no proof

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