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On the number of minimal completely separating systems and antichains in a Boolean lattice

Roberts, Ian T., Rylands, Leanne J., Montag, Terry and Gruettmueller, Martin (2010). On the number of minimal completely separating systems and antichains in a Boolean lattice. Australasian Journal of Combinatorics,48:143-158.

Document type: Journal Article
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IRMA ID 81704288xPUB217
Title On the number of minimal completely separating systems and antichains in a Boolean lattice
Author Roberts, Ian T.
Rylands, Leanne J.
Montag, Terry
Gruettmueller, Martin
Journal Name Australasian Journal of Combinatorics
Publication Date 2010
Volume Number 48
ISSN 1034-4942   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-78449266812
Start Page 143
End Page 158
Total Pages 15
Place of Publication Australia
Publisher Centre for Discrete Mathematics & Computing
HERDC Category C1 - Journal Article (DIISR)
Abstract An (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1,..., n} such that for all distinct a, b ∈ [n] there are blocks A, B ∈C with a ∈ A \ B and b ∈ B \ A. An (n)CSS is minimal if it contains the minimum possible number of blocks for a CSS on [n]. The number of non-isomorphic minimal (n)CSSs is determined for 11 ≤ n ≤ 35. This also provides an enumeration of a natural class of antichains.
Description for Link Link to published version
URL http://ajc.maths.uq.edu.au/pdf/48/ajc_v48_p143.pdf


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