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On a Combinatorial Problem in Number Theory

Published online by Cambridge University Press:  20 November 2018

Bernt Lindström*
Affiliation:
University of Stockholm
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Given an integer k ≤ 2 and a finite set M of rational integers. Let vi (i = 1, 2, …, n) be m-dimensional (column-)vectors with all components from M and such that the kn sums

1.1

are all different. Then we shall say that {v1, v2, …, vn} is a detecting set of vectors.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bellman, R. and Shapiro, H.N., On a problem in additive number theory, Ann. Math. (2)49(1948), 333-340.Google Scholar
2. Cantor, D. G., Determining a set from the cardinalities of its intersections with other sets, Canad, J. Math. 16 (1964), 94-97.Google Scholar
3. Clements, G. F. and Lindström, B., A sequence of (±l) - determinants with large values, Proc. Amer. Math. Soc. June 1965.Google Scholar
4. Erdös, P., Problems and results in additive number theory, Colloque sur la théorie des nombres, Bruxelles (1955), 127-137.Google Scholar
5. Erdös, P. and Rényi, A., On two problems of information theory, Publ. Hung. Acad. Sci. 8 (1963), 241-254.Google Scholar
6. Fine, N.J., Solution El 399, Amer. Math. Monthly 67 (1960), 697.Google Scholar
7. Lindström, B., On a combinatory detection problem, Publ. Hung. Acad. Sci. 9 (1964), 195-207.Google Scholar
8. Shapiro, H. S., Problem El 399, Amer. Math. Monthly 67 (1960) 82.Google Scholar
9. Sőderberg, S. and Shapiro, H. S., A combinatory detection problem, Amer. Math. Monthly 70 (1963), 1066-1070.Google Scholar