Article contents
Sidon Sets are Proportionally Sidon with Small Sidon Constants
Published online by Cambridge University Press: 11 December 2018
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 $n$-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.
Keywords
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2018
Footnotes
This research was supported in part by NSERC grant 2016-03719. This paper is in final form and no version of it will be submitted for publication elsewhere.
References
- 2
- Cited by