Cartesian Product of Sets Without Repeated Elements

In many applications, like database management systems, is very useful to have an expression to compute the cardinality of cartesian product of k sets without repeated elements; we designate this problem as T(k). The value of |T(k)| is upper-bounded by the multiplication of cardinalities of the sets. As long as we have searched, it has not been reported a general expression to compute T(k) using cardinalities of the intersections of sets, this is the main topic of this paper. Given three sets with indices {0,1,2}, Ci is the cardinality of one set, Ci,j (i更多