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arXiv · 1808.03128

Sidon sets are proportionally Sidon with small Sidon constants

Kathryn E. Hare·Robert·Yang
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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.

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Kathryn E. Hare, Robert, Yang. 2018-08-09. Sidon sets are proportionally Sidon with small Sidon constants. https://doi.org/10.4153/s0008439518000620

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