Resumen de Sidon set systems

Javier Cilleruelo , Oriol Serra , Maximilian Wötzel

• 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.