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

Ian T. Roberts; Leanne J. Rylands; Terry Montag; Martin Grüttmüller

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

Ian T. Roberts, Leanne J. Rylands, Terry Montag, Martin Grüttmüller

School of Computer, Data & Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 Ð„ C with a Ð„ A B and b Ð„ 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 â‰¤ n â‰¤ 35. This also provides an enumeration of a natural class of antichains.

Original language	English
Pages (from-to)	143-158
Number of pages	16
Journal	Australasian Journal of Combinatorics
Volume	48
Publication status	Published - 2010

Keywords

algebra, Boolean
mathematics

Cite this

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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 {\DH}„ C with a {\DH}„ A B and b {\DH}„ 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 {\^a}‰¤ n {\^a}‰¤ 35. This also provides an enumeration of a natural class of antichains.",

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author = "Roberts, {Ian T.} and Rylands, {Leanne J.} and Terry Montag and Martin Gr{\"u}ttm{\"u}ller",

year = "2010",

language = "English",

volume = "48",

pages = "143--158",

journal = "Australasian Journal of Combinatorics",

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T1 - On the number of minimal completely separating systems and antichains in a Boolean lattice

AU - Roberts, Ian T.

AU - Rylands, Leanne J.

AU - Montag, Terry

AU - Grüttmüller, Martin

PY - 2010

Y1 - 2010

N2 - An (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1,...,n} such that for all distinct a, b Ð„ C with a Ð„ A B and b Ð„ 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 â‰¤ n â‰¤ 35. This also provides an enumeration of a natural class of antichains.

AB - An (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1,...,n} such that for all distinct a, b Ð„ C with a Ð„ A B and b Ð„ 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 â‰¤ n â‰¤ 35. This also provides an enumeration of a natural class of antichains.

KW - algebra, Boolean

KW - mathematics

UR - http://handle.uws.edu.au:8081/1959.7/551718

M3 - Article

SN - 1034-4942

VL - 48

SP - 143

EP - 158

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

ER -

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

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