Complementing sets of -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 | References | Similar Articles | Additional Information

Abstract: Let *S*, be finite nonempty sets of *n*-tuples of integers such that, if , for , then , and such that every has a unique representation as a sum with . If *S* is the cartesian product of *n* sets of integers, then each is also the cartesian product of *n* sets of integers, and conversely.

**[1]**Rodney T. Hansen,*Complementing pairs of subsets of the plane*, Duke Math. J.**36**(1969), 441–449. MR**0244404****[2]**Ivan Niven,*A characterization of complementing sets of pairs of integers*, Duke Math. J.**38**(1971), 193–203. MR**0274414**

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Additional Information

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