A note on minimal additive complements of integers

Let C,W⊆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. We provide a partial answer to a question posed by Kiss, Sándor, and Yang regarding the minimal additive complement...

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Bibliographic Details
Published in:Discrete mathematics 2019-07, Vol.342 (7), p.1912-1918
Main Author: Kwon, Andrew
Format: Article
Language:English
Subjects:
Additive complements
Eventually periodic sets
Minimal complements
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Summary:Let C,W⊆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. We provide a partial answer to a question posed by Kiss, Sándor, and Yang regarding the minimal additive complement of sets of the form W=(A+nN)∪F∪G, where |F|
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.03.010