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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Complementing sets of $ n$-tuples of integers


Author: Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 34 (1972), 71-72
MSC: Primary 10L05
DOI: https://doi.org/10.1090/S0002-9939-1972-0294286-7
MathSciNet review: 0294286
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Abstract: Let S, $ {A_1},{A_2}, \cdots ,{A_p}$ be finite nonempty sets of n-tuples of integers such that, if $ {a_i} \in {A_i}$, for $ i = 1,2, \cdots ,p$, then $ {a_1} + {a_2} + \cdots + {a_p} \in S$, and such that every $ s \in S$ has a unique representation as a sum $ s = {a_1} + {a_2} + \cdots + {a_p}$ with $ {a_i} \in {A_i}$. If S is the cartesian product of n sets of integers, then each $ {A_i}$ is also the cartesian product of n sets of integers, and conversely.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294286-7
Keywords: Complementing sets, sumsets of integers, addition of n-tuples of integers
Article copyright: © Copyright 1972 American Mathematical Society