Set systems with distinct sumsets
- Publication date
- Publisher
- 'Elsevier BV'
Abstract
A family A of k-subsets of {1,2,…,N} is a Sidon system if the sumsets A+A′, A,A′∈A are pairwise distinct.
We show that the largest cardinality Fk(N) of a Sidon system of k-subsets of [N] satisfies Fk(N)≤(k−1N−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 and 3.Peer Reviewe