On Set Coverings in Cartesian Product Spaces
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Appendix: On Set Coverings in Cartesian Product Spaces
Consider (X, E), where X is a finite set and E is a system of subsets whose union equals X. For every natural number n ∈ N define the cartesian products Xn = ∏n 1 X and En = ∏n 1 E . The following problem is investigated: how many sets of En are needed to cover Xn? Let this number be denoted by c(n). It is proved that for all n ∈ N exp{C · n} ≤ c(n) ≤ exp{Cn+ log n+ log log |X|}+ 1. A formula f...
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