整数群上一类和超差集合的构造

A construction of sets with more sums than differences of integers

考虑了整数群子集自身和及自身差势的问题,基于对前人给出的几类整数群上超差集合构造的研究,通过对典型有限和超差集合A1的有限分解,即A1={0,2}∪{3,7,11,…,4k-1}∪{4k,4k+2}∪{4},其中k是不小于3的正整数,证明给出了整数群上一类无限的和超差集合的构造,使集合的势从有限上升为无限,拓展了前人的理论成果。

This paper discusses the problem of the cardinality of the sums and differences of subsets of integers. It researches the constructions of some sets with more sums than differences of integers that were given by predecessors. A typical finite set A1 is decomposed, that is, A1={0, 2}∪ {3, 7, 11,…, 4k-1} ∪{4k, 4k＋2} ∪ {4}, here k is integer and k≥3. The paper also gives out a construction of infinite sets with more sums than differences of integers, making the cardinality of the sets from finiteness rise to infiniteness and extending predecessors＇ theoretically achievements.