%0 Journal Article
%T Constructions of Generalized Sidon Sets
%A Greg Martin
%A Kevin O'Bryant
%J Mathematics
%D 2004
%I arXiv
%R 10.1016/j.jcta.2005.04.011
%X We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k=s_1+s_2, s_i\in S; such sets are called Sidon sets if g=2 and generalized Sidon sets if g\ge 3. We extend to generalized Sidon sets the Sidon-set constructions of Singer, Bose, and Ruzsa. We also further optimize Koulantzakis' idea of interleaving several copies of a Sidon set, extending the improvements of Cilleruelo & Ruzsa & Trujillo, Jia, and Habsieger & Plagne. The resulting constructions yield the largest known generalized Sidon sets in virtually all cases.
%U http://arxiv.org/abs/math/0408081v2