Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcta.2013.05.001
Title: An analogue of the Hilton-Milner theorem for set partitions
Authors: Ku, C.Y. 
Wong, K.B.
Keywords: Erdos-Ko-Rado
Hilton-Milner
Intersecting family
Set partitions
Issue Date: Sep-2013
Citation: Ku, C.Y., Wong, K.B. (2013-09). An analogue of the Hilton-Milner theorem for set partitions. Journal of Combinatorial Theory. Series A 120 (7) : 1508-1520. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcta.2013.05.001
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 B n 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] {set minus} {i, n}}. This is an analogue of the Hilton-Milner theorem for set partitions. © 2013 Elsevier Inc.
Source Title: Journal of Combinatorial Theory. Series A
URI: http://scholarbank.nus.edu.sg/handle/10635/102816
ISSN: 00973165
DOI: 10.1016/j.jcta.2013.05.001
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