Please use this identifier to cite or link to this item:
https://doi.org/10.1016/j.jcta.2013.05.001
DC Field | Value | |
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dc.title | An analogue of the Hilton-Milner theorem for set partitions | |
dc.contributor.author | Ku, C.Y. | |
dc.contributor.author | Wong, K.B. | |
dc.date.accessioned | 2014-10-28T02:30:02Z | |
dc.date.available | 2014-10-28T02:30:02Z | |
dc.date.issued | 2013-09 | |
dc.identifier.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 | |
dc.identifier.issn | 00973165 | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/102816 | |
dc.description.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. | |
dc.description.uri | http://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.jcta.2013.05.001 | |
dc.source | Scopus | |
dc.subject | Erdos-Ko-Rado | |
dc.subject | Hilton-Milner | |
dc.subject | Intersecting family | |
dc.subject | Set partitions | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1016/j.jcta.2013.05.001 | |
dc.description.sourcetitle | Journal of Combinatorial Theory. Series A | |
dc.description.volume | 120 | |
dc.description.issue | 7 | |
dc.description.page | 1508-1520 | |
dc.description.coden | JCBTA | |
dc.identifier.isiut | 000323868200010 | |
Appears in Collections: | Staff Publications |
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