On minimal additive complements of integers

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:162

Article

Kiss, Sandor Z.¹  Sandor, Csaba¹  Yang, Quan-Hui² 

[1] Budapest Univ Technol & Econ, Inst Math, H-1529 Budapest, Hungary

[2] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Jiangsu, Peoples R China

关键词: Additive complements;    Minimal complements;    Periodic sets;   

DOI  :  10.1016/j.jcta.2018.11.011

来源: Elsevier

【 摘 要 】

Let C, W subset of Z. If C + W = Z, then the set C is called an additive complement to W in Z. If no proper subset of C is an additive complement to W, then C is called a minimal additive complement. Let X subset of N. If there exists a positive integer T such that x + T is an element of X for all sufficiently large integers x is an element of X, then we call X eventually periodic. In this paper, we study the existence of a minimal complement to W when W is eventually periodic or not. This partially answers a problem of Nathanson. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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