Restricted sumsets in Z_n

摘要

Let h >= 2 be a positive integer. For any subset A subset of Z(n), let h <^> A be the set of the elements of Z(n) which are sums of h distinct elements of A. In this paper, we obtain some new results on 4. A. For example, we show that if vertical bar A vertical bar >= 0.4045n and n is odd, then 4<^>A = Z(n); under some conditions, if n is even and vertical bar A vertical bar is close to n/4, then 4 <^> A = Z(n).