2026/06/30 by Kevin O'Bryant · 1 citation
Mathematics · #math.CO #math.NT
Let g ≥1. A set A of nonnegative integers is a Sidon set if for each d>0 there is at most one pair (a,b) ∈ A × A with d=a-b. If there are at most g pairs, then A is a g-Golomb ruler. We prove that if A is a g-Golomb ruler, then \liminfn→∞ ( | A∩[0,n) | )/(√(n/log n)) ≤ (2√ g )/(√(log 2)), generalizing and sharpening results of Erdős and Cilleruelo. There is a g-Golomb ruler G with (√ g )/(√2) ≤ \limsupn→∞ ( | G∩[0,n) | )/(√ n) ≤ √(g ) , generalizing a result of Krückeberg.