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Partitions of the Natural Numbers

Published online by Cambridge University Press:  20 November 2018

Myer Angel
Myer Angel*
Affiliation:
McGill University
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We obtain in this article some results concerning partitions of the naturalnumbers, the most important of which is a generalization of that quotedimmediately below. Some intuitive material is included.

In 1954, J. Lambek and L. Moser [l] showed that "Two non-decreasingsequences f and g (of non-negative integers) are inverses if and only if thecorresponding sets F and G of positive integers, defined by F(m) = the mthelement of F = f(m) + m and G(n) = g(n) + n are complementary."

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 219 - 236
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Lambek, J. and Moser, L., Inverse and Complementary Sequences of Natural Numbers, Amer. Math. Monthly, Vol.61, No.7, 1954, pp.454–458.Google Scholar