| 孙翠芳,余明韬.整数中限制符号和集的一些逆问题[J].数学年刊A辑,2024,45(3):259~274 |
| 整数中限制符号和集的一些逆问题 |
| Some Inverse Problems for Restricted Signed Sumsets in Integers |
| Received:October 24, 2023 Revised:November 13, 2024 |
| DOI：10.16205/j.cnki.cama.2024.0018 |
| 中文关键词: 和集 限制符号和集 逆问题 |
| 英文关键词:Sumset Restricted signed sumset Inverse problems |
| 基金项目:国家自然科学基金(No.12371003) |
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| 中文摘要: |
| 设k,h是正整数,满足h≤k.设A={a0,a1,…,ak-1}是加性阿贝尔群的子集,■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2±∧A接近下界时,集合A的结构. |
| 英文摘要: |
| Let k,h be positive integers withh≤k.Let A={a0,a1,…,ak-1}be a subset of an additive abelian group and h^±A={k-1∑i=0λiai:λi∈{-1,0,1},i=0,1,…,k-1,k-1∑i=0|λi|=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. |
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