Constructions of generalized Sidon sets

2004/08/31 by Greg Martin, Kevin O’Bryant, Kevin O'Bryant · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Numerical Analysis Techniques #Rough Sets and Fuzzy Logic #math.CO #math.NT #msc:05B10 #msc:11B34

paper · pdf · doi:10.1016/j.jcta.2005.04.011

published as J. Combin. Theory Ser. A 113 (2006), no. 4, 591--607. · 15 pages, 1 figure (revision fixes typos, adds a few details, and adjusts notation)

arxiv created 2005/02/21 · openalex publication_date 2005/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k=s₁+s₂, s_i∈ S; such sets are called Sidon sets if g=2 and generalized Sidon sets if g≥ 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.

Citations

• Continuous Ramsey Theory and Sidon Sets
• The Difference Between Consecutive Primes
• The Difference Between Consecutive Primes, II

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• Generalized Sidon sets
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