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Determining a Set from the Cardinalities of its Intersections with Other Sets

Published online by Cambridge University Press:  20 November 2018

David G. Cantor
David G. Cantor*
Affiliation:
University of Washington, Seattle, Washington
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Let n be a positive integer and put N = {1, 2, . . . , n}. A collection {S1, S2, . . . , St} of subsets of N is called determining if, for any T ⊂ N, the cardinalities of the t intersections T ∩ Sj determine T uniquely. Let €1, €2, . . . , €n be n variables with range {0, 1}. It is clear that a determining collection {Sj) has the property that the sums

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 94 - 97
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Fine, N. J., Solution E1399, Amer. Math. Monthly, 67 (1960), 697.Google Scholar
2. Shapiro, H. S., Problem E1399, Amer. Math. Monthly, 67 (1960), 82.Google Scholar