2026/07/24 by Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu
Mathematics · #Limits and Structures in Graph Theory #Graph theory and applications #Point processes and geometric inequalities
paper · doi:10.1112/blms.70452
Abstract 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.