Sidon set systems

Javier Cilleruelo ^[1] ; Oriol Serra ^[1] ; Maximilian Wötzel ^[1]
1. [1] Universitat Politècnica de Catalunya
  
  Universitat Politècnica de Catalunya
  
  Barcelona, España
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 5, 2020, págs. 1527-1548
Idioma: inglés
DOI: 10.4171/rmi/1174
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Resumen
- A family A of k-subsets of {1,2,…,N} is a Sidon system if the sumsets A+B, A,B∈A are pairwise distinct. We show that the largest cardinality Fk(N) of a Sidon system of k-subsets of [N] satisfies Fk(N)≤(N−1k−1)+N−k and the asymptotic lower bound Fk(N)=Ωk(Nk−1). More precise bounds on Fk(N) are obtained for k≤3. We also obtain the threshold probability for a random system to be Sidon for k≥2.