Upper and lower bounds for finite Bh[g] sequences

[摘要] We give a non-trivial upper bound for F-h,(g,N), the size of a B-h[g] subset of {1,...,N}, when g > 1. In particular, we prove F-2(g,N) less than or equal to 1.864(gN)(1/2) + 1, and F-h(g,N) less than or equal to 1/(1+cos(h)(pi/h))(1/h) (hh!gN)(1/h) > 2. On the other hand, we exhibit B-2[g] subsets of {1,...,N} with g+[g/2]/rootg+2[g/2] N-1/2 + o(N-1/2), elements. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01