Characterizing Sidon sets by interpolation properties of subsets
Volume 112 / 2008
Colloquium Mathematicum 112 (2008), 175-199
MSC: Primary 42A55, 43A46; Secondary 43A25.
DOI: 10.4064/cm112-2-1
Abstract
Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized $I_0$-subsets in a uniform way, again in groups containing but a finite number of elements of order 2.
