Sidon set systems

Abstract

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 F k (N ) of a Sidon system of k-. More precise bounds on F k (N ) are obtained for k ≤ 3. We also obtain the threshold probability for a random system to be Sidon for k ≥ 2.This upper bound is tight for k = 2, that is, F 2 (N ) = 2N − 3. We believe that it is asymptotically sharp for any k ≥ 2, but we are only able to prove this for k = 2 and k = 3. For k ≥ 4, we prove that N k−1 is the right order of magnitude.Mathematics Subject Classification (2010): Primary 11B13; Secondary 05B10.

Sidon sets for linear forms

“…For surveys of classical Sidon sets, see Halberstam and Roth [2] and O'Bryant [7]. For recent work, see [1,3,4,5,6,8,9,11,13].…”