Restricted sumsets in ℤn

Abstract

Let [Formula: see text] be a positive integer. For any subset [Formula: see text], let [Formula: see text] be the set of the elements of [Formula: see text] which are sums of [Formula: see text] distinct elements of [Formula: see text]. In this paper, we obtain some new results on [Formula: see text]. For example, we show that if [Formula: see text] and [Formula: see text] is odd, then [Formula: see text]; under some conditions, if [Formula: see text] is even and [Formula: see text] is close to [Formula: see text], then [Formula: see text].