2022/03/24 by Eric Naslund, Naslund, Eric
Computer Science · Mathematics · #05C65 (Secondary) #05D05 (Primary) 15A03 #15A69 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2203.13370
openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For k≥3, a collection of k sets is said to form a weak Δ-system if the intersection of any two sets from the collection has the same size. Erdős and Szemerédi asked about the size of the largest family F of subsets of \1,…,n\ that does not contain a weak Δ-system. In this note we improve upon the best upper bound of the author and Sawin from arXiv:1606.09575 and show that |F|≤((2)/(3)Θ(C)+o(1))n where Θ(C) is the capset capacity. In particular, this shows that |F|≤(1.8367…+o(1))n.