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Weighted Sidon sets

1976; Mathematical Sciences Publishers; Volume: 63; Issue: 1 Linguagem: Inglês

10.2140/pjm.1976.63.255

1945-5844

J. E. Sanders,

Limits and Structures in Graph Theory

A weighted generalisation of Sidon sets, PΓ-Sidon sets, is introduced and studied for compact abelian groups.Firstly TF-Sidon sets are characterised analogously to Sidon sets and variations of these characterisations shown to lead back to Sidon sets.For the circle group PΓ-Sidon sets are constructed which are not Λ(l) and hence not Sidon.The algebra of all W'a making a set TΓ-Sidon is investigated and Sidon and p-Sidon sets cast in terms of it.Finally analytic properties of TF-Sidon sets are pursued and a necessary condition on the growth of W 2 obtained.