Counting Set Systems by Weight
نویسندگان
چکیده
منابع مشابه
Counting Set Systems by Weight
Applying enumeration of sparse set partitions, we show that the number of set systems H ⊂ exp({1, 2, . . . , n}) such that ∅ 6 ∈ H, ∑E∈H |E| = n and ⋃E∈H E = {1, 2, . . . ,m}, m ≤ n, equals (1/ log(2)+ o(1))bn where bn is the n-th Bell number. The same asymptotics holds if H may be a multiset. If the vertex degrees in H are restricted to be at most k, the asymptotics is (1/αk + o(1))bn where αk...
متن کاملA pr 2 00 4 Counting set systems by weight
Applying the enumeration of sparse set partitions, we show that the number of set systems H ⊂ exp({1, 2, . . . , n}) such that ∅ 6∈ H, ∑E∈H |E| = n and ⋃ E∈H E = {1, 2, . . . ,m}, m ≤ n, equals (1/ log(2)+o(1))bn where bn is the n-th Bell number. The same asymptotics holds ifH may be a multiset. If vertex degrees in H are restricted to be at most k, the asymptotics is (1/αk + o(1)) bn where αk ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1908