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- W2167233799 abstract "Let B(n) denote the collection of all set partitions of [n]. Suppose A⊆B(n) is a non-trivial t-intersecting family of set partitions i.e. any two members of A have at least t blocks in common, but there is no fixed set of t blocks of size one which belong to all of them. It is proved that for sufficiently large n depending on t,|A|⩽Bn−t−B˜n−t−B˜n−t−1+t where Bn is the n-th Bell number and B˜n is the number of set partitions of [n] without blocks of size one. Moreover, equality holds if and only if A is equivalent to{P∈B(n):{1},{2},…,{t},{i}∈Pfor somei∉{1,2,…,t,n}}∪{Q(i,n):1⩽i⩽t} where Q(i,n)={{i,n}}∪{{j}:j∈[n]∖{i,n}}. This is an analogue of the Hilton–Milner theorem for set partitions." @default.
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- W2167233799 date "2013-09-01" @default.
- W2167233799 modified "2023-10-18" @default.
- W2167233799 title "An analogue of the Hilton–Milner theorem for set partitions" @default.
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- W2167233799 doi "https://doi.org/10.1016/j.jcta.2013.05.001" @default.
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