2024/11/12 by Kevin O’Bryant, O'Bryant, Kevin · 1 citation
Computer Science · Engineering · Mathematics · #11B13 (Primary) 05B10 #11Y99 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2411.08139
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let SPP(n) be the set \(|A+A|,|A A|) : A⊆ \mathbb N, |A|=n\ of sum-product pairs, where A+A is the sumset \a+b : a,b∈ A\ and A A is the product set \ab:a,b∈ A\. We construct a dataset consisting of 1162868 sets whose sum-product pairs are at least 84% of SPP(n) for each n≤ 32. Notably, we do **not** see evidence in favor of Erdős's Sum-Product Conjecture in our dataset. For n≤ 6, we prove the exact value of SPP(n). We include a number of conjectures, open problems, and observations motivated by this dataset, a large number of color visualizations.