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Orbits of antichains revisited

✍ Scribed by P.J Cameron; D.G Fon-Der-Flaass

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 472 KB
Volume: 16
Category: Article
ISSN: 0195-6698
DOI: 10.1016/0195-6698(95)90036-5

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📜 SIMILAR VOLUMES

Orbits of Antichains in Ranked Posets

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We consider the permutation \(f\) of antichains of a ranked poset \(P\), moving the set of lower units of any monotone boolean function on \(P\) to the set of its upper zeros. A duality relation on orbits of this permutation is found, which is used for proving a conjecture by M. Deza and K. Fukuda.

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A subset A of an ordered set P is a cutset if each maximal chain of P meetsA ; if, in addition, A is an antichain call it an antichain cutset. Our principal result is a characterization, by means of a 'forbidden configuration', of those finite ordered sets, which can be expressed as the union of ant