Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Complementing sets of $n$-tuples of integers
HTML articles powered by AMS MathViewer

by Melvyn B. Nathanson PDF
Proc. Amer. Math. Soc. 34 (1972), 71-72 Request permission

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.
References
  • Rodney T. Hansen, Complementing pairs of subsets of the plane, Duke Math. J. 36 (1969), 441–449. MR 244404
  • Ivan Niven, A characterization of complementing sets of pairs of integers, Duke Math. J. 38 (1971), 193–203. MR 274414
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10L05
  • Retrieve articles in all journals with MSC: 10L05
Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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