Research demonstrates asymptotic behavior of regular simplices in higher dimensions, resolving a conjecture.
We study the extremal function , defined as the maximum number of regular ‐simplices spanned by points in . For any fixed , we determine the asymptotic behavior of up to a lower‐order term. In particular, when , we determine the exact value of , for all even dimensions and sufficiently large . This resolves a conjecture of Erdős in a stronger form. The proof leverages techniques from hypergraph Turán theory and linear algebra.
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Clemen et al. (2026) studied this question.
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