Geodesic
On The Determination of Sets by Sets of Sums of Fixed Order
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 596-611

Voir la notice de l'article provenant de la source Cambridge University Press

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.” 
Ewell, John A. On The Determination of Sets by Sets of Sums of Fixed Order. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 596-611. doi: 10.4153/CJM-1968-059-6
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[1] 1. Bôcher, M., Introduction to higher algebra (McMillan, New York, 1924). Google Scholar

[2] 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] 3. MacMahon, P. A., Combinatory analysis (Chelsea, New York, 1960). Google Scholar

[4] 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

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