Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-29T02:51:39.020Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Problem in Partial Difference Equations

Published online by Cambridge University Press:  20 November 2018

Calvin T. Long
Calvin T. Long*
Affiliation:
Washington State University, Pullman, Washington
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.

The purpose of this paper is not to solve a problem but to pose one that may be of some interest, depth, and consequence.

Given that the positive integer n has the canonical representation n = Πhi=1 piαi the problem of finding the number F(n) = f(α1, α2, … αn) of ordered factorizations of n into positive nontrivial integral factors is equivalent to that of finding the number of ordered partitions of the vector (α1, α2, … αn) into nonzero vectors with nonnegative integral components.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 3 , September 1970 , pp. 333 - 335
Copyright
Copyright © Canadian Mathematical Society 1970

Footnotes

(1)

This work was supported by National Science Foundation Grant GP-7114.

References

1. Carlitz, L. and Moser, L., On some special factorizations of (1 - xn)/(1 - x), Canad. Math. Bull. 9 (1966), 421-426.Google Scholar
2. Long, C. T., Addition theorems for sets of Integers, Pac. J. Math. 23 (1967), 107-112.Google Scholar
3. MacMahon, P. A., The theory of perfect partitions and the compositions of multipartite numbers, Philos. Trans. Roy. Soc. London (A), 184 (1893), 835-901.Google Scholar