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Title: Constructions of Generalized Sidon Sets
Authors: Greg Martin, Kevin O'Bryant
Categories: math.NT Number Theory (math.CO Combinatorics)
Comments: 15 pages, 1 figure (revision fixes typos, adds a few details, and adjusts notation)
MSC: 11B34; 05B10
Journal reference: J. Combin. Theory Ser. A 113 (2006), no. 4, 591--607. (DOI)
Abstract: 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.
Owner: Kevin O'Bryant
Version 1: Thu, 5 Aug 2004 23:58:08 GMT
Version 2: Mon, 21 Feb 2005 08:05:49 GMT