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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
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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 = Πh i=1 pi αi 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.

Information

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