整数中限制符号和集的一些逆问题  

Some Inverse Problems for Restricted Signed Sumsets in Integers

作　　者：孙翠芳 佘明韬 SUN Cuifang;SHE Mingtao(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,Anhui,China.)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《数学年刊(A辑)》2024年第3期259-274,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12371003)的资助.

摘　　要：设k,h是正整数,满足h≤k.设A={a_(0),a_(1),…,a_(k-1)}是加性阿贝尔群的子集,h^±A={k-1∑i=0λ_(i)a_(i):λ_(i)∈{-1,0,1},i=0,1,…,k-1,k-1∑i=0|λ_(i)|=h}是A的h阶限制符号和集.本文中,作者确定了当A是有限的正整数集,并且A的限制符号和集2A接近下界时,集合A的结构.Let k,h be positive integers withh≤k.Let A={a_(0),a_(1),…,a_(k-1)}be a subset of an additive abelian group and h^±A={k-1∑i=0λ_(i)a_(i):λ_(i)∈{-1,0,1},i=0,1,…,k-1,k-1∑i=0|λ_(i)|=h}be the h-fold restricted signed sumset of A.In this paper,the authors determine the structure of the set A when A is a finite set of positive integers and the restricted signed sumset 2±A has size closer to the lower bound.

关 键 词：和集 限制符号和集 逆问题 

分 类 号：O156[理学—数学]