关于符号和集的一些注记

Some Remarks on Signed Sumsets

设Z是整数集,h,k是正整数.对交换加群G的任意有限非空子集A={a_(0),a_(1),…,a_(k-1)},称■为A的h阶符号和集.本文给出当A{a_(k-1)}是特定的等差数列时,符号和集h_±A的基数如何随着最大元素ak-1的增加而变化的一些结果.

Let Z be the set of all integers and k,h be positive integers.For any nonempty finite subset A={a_(0),a_(1),…,a_(k-1)}of an additive abelian group G,let■be the h-fold signed sumset of A.In this paper,we will give some results about how the cardinality of the signed sumset h_±A changes as the largest element a_(k-1)increases when A{a_(k-1)}is a special arithmetic progression.