Constructions of Generalized Sidon Sets

Details Constructions of Generalized Sidon Sets Constructions of Generalized Sidon Sets

2004-08-05

arxiv.org/abs/math/0408081v2

J. Combin. Theory Ser. A 113 (2006), no. 4, 591--607.

Mathematics

Number Theory

15 pages, 1 figure (revision fixes typos, adds a few details, and adjusts notation)

Scientific paper

10.1016/j.jcta.2005.04.011

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.

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