ON B2K-SEQUENCES

A set A of nonnegative integers is called a B(h)-sequence if all sums x1 + ... + x(h) with x(i) is-an-element-of A and x1 less-than-or-equal-to ... less-than-or-equal-to x(h) 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 inf(n --> infinity) A(n)2k square-root (log n)/n < infinity, provided A(n2) much less than A(n)2 for all n sufficiently large, where A(n) is the number of positive elements less-than-or-equal-to n in A. (C) 1994 Academic Press, Inc.