# zbMATH — the first resource for mathematics

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
##### Keywords:
set partitions; Bell numbers
Full Text: