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OP-12150Status unassessedGeometry and topology

Max to min ratios (AlphaEvolve problem 50)

Max to min ratios (AlphaEvolve problem 50). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 52C10 · Erd?s problems and related topics of discrete geometry

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
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Problem statement

Let n,d≥2n,d \geq 2. Let C(d,n)C(d,n) denote the largest quantity such that, given any nn distinct points x1,…,xnx_1,\dots,x_n in Rd\R^d, the maximum distance max⁡1≤i<j≤n∥xi−xj∥\max_{1 \leq i < j \leq n} \|x_i-x_j\| between the points is at least C(d,n)C(d,n) times the minimum distance min⁡1≤i<j≤n∥xi−xj∥\min_{1 \leq i < j \leq n} \|x_i-x_j\|. Establish upper and lower bounds for C(d,n)C(d,n). What are the configurations that attain the minimal ratio between the two distances?

Lean 4

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Background

Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.30 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864.

Progress & source assessment

The repository page records no bounds for this problem.

References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Max to min ratios (AlphaEvolve problem 50) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

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Discussion

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