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Counting set systems by weight. (English) Zbl 1065.05016
It is well known that the Bell numbers count the total number of ways a set of \(n\) elements can be partitioned into nonempty, mutually disjoint subsets. This paper considers the situation when the subsets may intersect. The main result states that such a number is asymptotically larger than the Bell number by an exponential factor. The enumeration problem can also be formulated as counting 0-1 matrices satisfying certain properties.

MSC:
05A18 Partitions of sets
05A16 Asymptotic enumeration
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