The number of regular simplices in higher dimensions
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.
Authors
- Felix Christian Clemen (ORCID: https://orcid.org/0000-0002-3798-1645)
- Dingyuan Liu
- Adrian Dumitrescu
Institutions
- Karlsruhe Institute of Technology (DE)
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- University of Bucharest (RO)
- University of Victoria (CA)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-07-24
- DOI
- https://doi.org/10.1112/blms.70452
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Pacific Institute for the Mathematical Sciences