On Finite Sidon Sequences

AbstractA set A of integers is called a Bh-sequence if all sums a1 + · · · + ah, where ai ∈ A, are distinct up to rearrangement of the summands. Let Fh(n) (resp. ƒh(n)) denote the size of a largest Bh-sequence (resp. Bh-sequence for Z/(n)). It is proved that, for every r ≥ 1 as n → ∞, F2r(n) ≤ r1/(2r)(r!)1/rn1/(2r) + O(n1/(4r)). Some open problems concerning Bh-sequences are also discussed in this paper