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Title: On cross-intersecting families of set partitions
Authors: Ku, C.Y. 
Wong, K.B.
Keywords: Cross-intersecting family
Set partitions
Issue Date: 31-Dec-2012
Citation: Ku, C.Y.,Wong, K.B. (2012-12-31). On cross-intersecting families of set partitions. Electronic Journal of Combinatorics 19 (4) : -. ScholarBank@NUS Repository.
Abstract: Let B(n) denote the collection of all set partitions of [n]. Suppose A1, A2 ⊆ B(n) are cross-intersecting i.e. for all A1 ∈ A1 and A2 ∈ A2, we have A1 ∩ A2 ≠ {circled division slash}. It is proved that for sufficiently large n, |A1| |A2| ≤ B2 n-1 where Bn is the n-th Bell number. Moreover, equality holds if and only if A1 = A2 and A1 consists of all set partitions with a fixed singleton.
Source Title: Electronic Journal of Combinatorics
ISSN: 10778926
Appears in Collections:Staff Publications

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