Determining a Set from the Cardinalities of its Intersections with Other Sets
David G. Cantor · Canadian Journal of Mathematics · 1964
Let n be a positive integer and put N = {1, 2, . . . , n }. A collection { S 1 , S 2 , . . . , S t } of subsets of N is called determining if, for any T ⊂ N , the cardinalities of the t intersections T ∩ S j determine T uniquely. Let € 1 , € 2 , . . . , € n be n variables with range {0, 1}. It is clear that a determining collection { S j ) has the property that the sums