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OP-12137Status unassessedCombinatorics

The hypergraph Turán number of the tetrahedron (AlphaEvolve problem 37)

The hypergraph Turán number of the tetrahedron (AlphaEvolve problem 37). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 05C65 · HypergraphsMSC 05C35 · Extremal problems in graph theory

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 CC be the largest quantity such that, as n→∞n \to \infty, one can locate a 33-uniform hypergraph on nn vertices and at least (C−o(1))(n3)(C-o(1)) \binom{n}{3} edges that contains no copy of the tetrahedron K4(3)K^{(3)}_4. What is CC?

Lean 4

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Background

The repository status chart does not categorize this problem. See Section 6.20 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

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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). — The hypergraph Turán number of the tetrahedron (AlphaEvolve problem 37) linkApache-2.0 (repository license); problem pages reproduced with attribution.

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