Abstract :
A set A of nonnegative integers is called a Bh-sequence if all sums x1 + · · · + xh with xi set membership, variant A and x1 ≤ · · · ≤ xh are distinct. Some results concerning the growth of the counting function of B2k-sequences are proved in the paper, including the following result: For any B2k-sequence A, lim infn → ∞A(n)[formula] < ∞, provided A(n2) much less-than A(n)2 for all n sufficiently large, where A(n) is the number of positive elements ≤ n in A.
