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On The Determination of Sets by Sets of Sums of Fixed Order

Published online by Cambridge University Press:  20 November 2018

John A. Ewell
John A. Ewell*
Affiliation:
York University, Toronto, Ontario
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The present investigation is based on two papers: “On the determination of numbers by their sums of a fixed order,” by J. L. Self ridge and E. G. Straus (4), and “On the determination of sets by the sets of sums of a certain order,” by B. Gordon, A. S. Fraenkel, and E. G. Straus (2).

First of all, we explain the terms implicit in the above titles. Throughout these considerations we use the term “set” to mean “a totality having possible multiplicities,” so that two sets will be counted as equal if, and only if, they have the same elements with identical multiplicities. In the most general sense the term “numbers” of (4) can be replaced by “elements of any given torsioniree Abelian group.”

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 596 - 611
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This paper is a condensation of the author's doctoral dissertation written under the direction of Professor E. G. Straus.

References

1. Bôcher, M., Introduction to higher algebra (McMillan, New York, 1924).Google Scholar
2. Gordon, B., Fraenkel, A. S., and Straus, E. G., On the determination of sets by the sets of sums of a certain order, Pacific J. Math., 12, No. 1 (1962).Google Scholar
3. MacMahon, P. A., Combinatory analysis (Chelsea, New York, 1960).Google Scholar
4. Selfridge, J. L. and Straus, E. G., On the determination of numbers by their sums of a fixed order, Pacific J. Math., 8, No. 4 (1958).Google Scholar