Sidon sets are proportionally Sidon with small Sidon constants
Functional Analysis
2019-11-13 v1
Abstract
In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was shown that Sidon sets were proportionally `special' Sidon in several other ways. Here, we prove that Sidon sets in torsion-free groups are proportionally -degree independent, a higher order of independence than quasi-independence, and we use this to prove that Sidon sets are proportionally Sidon with Sidon constants arbitrarily close to one, the minimum possible value.
Cite
@article{arxiv.1808.03128,
title = {Sidon sets are proportionally Sidon with small Sidon constants},
author = {Kathryn E. Hare and Robert and Yang},
journal= {arXiv preprint arXiv:1808.03128},
year = {2019}
}