Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T23:05:53.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Partitions of the Natural Numbers

Published online by Cambridge University Press:  20 November 2018

Myer Angel
Myer Angel*
Affiliation:
McGill University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain in this article some results concerning partitions of the natural numbers, the most important of which is a generalization of that quoted immediately below. Some intuitive material is included.

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

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