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

Ian Roberts, Leanne J Rylands, Terry Montag, Martin Gruttmuller

    Research output: Contribution to journalArticlepeer-review

    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.
    Original languageEnglish
    Pages (from-to)143-158
    Number of pages16
    JournalAustralasian Journal of Combinatorics
    Volume48
    Publication statusPublished - 2010

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