2023/10/30 by Daniel Carter, Zach Hunter, Carter, Daniel +3 · 1 citation
Mathematics · #05B10 (Primary) 11B50 #11B83 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2310.20032
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or B2 set) with k elements is at least k2-b k3/2-O(k) where b≤ 1.96365, a comparatively large improvement on past results. Equivalently, a Sidon set with diameter n has at most n1/2+0.98183n1/4+O(1) elements. The proof is conceptually simple but very computationally intensive, and the proof uses substantial computer assistance. We also provide a proof of b≤ 1.99058 that can be verified by hand, which still improves on past results. Finally, we prove that g-thin Sidon sets (aka g-Golomb rulers) with k elements have diameter at least g-1 k2 - (2-ε)g-1k3/2 - O(k), with ε≥ 0.02g-2.