Existence of a Sidon set for the distinct distance constant

2025/05/27 by Riblet, Robin, Schehr, Titien
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.20851

Abstract

We highlight a certain compactness of Sidon sets and B₂[g]-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose reciprocal sum is equal to the distinct distance constant, which answers a question from Guy and Zhang. We also improve the best known upper bound for this constant.

Citations

• On the Diameter of Finite Sidon Sets
• An upper bound on the size of Sidon sets
• A Complete Annotated Bibliography of Work Related to Sidon Sequences

Related

• One conjecture about size of Sidon sets
• An upper bound on the size of Sidon sets
• On large Sidon sets
• A numerical note on upper bounds for b 2 [g] sets
• On the Thickness of Infinite Generalized Sidon Sets, II