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The apparent structure of dense Sidon sets

  title={The apparent structure of dense Sidon sets},
  author={Sean Eberhard and Freddie Manners},
. The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets of abelian groups come from projective planes through a similar construction. We classify the Sidon sets arising in this man- ner from desarguesian planes and find essentially no new examples. There are many further examples arising from nondesarguesian planes. We conjecture that all dense Sidon sets arise from finite… 
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