Cameron, P. J.; Fon-Der-Flaass, D. G. Orbits of antichains revisited. (English) Zbl 0831.06001 Eur. J. Comb. 16, No. 6, 545-554 (1995). Summary: We present a new treatment of the permutation \(f\) of antichains in ranked posets moving the set of lower units of a monotone Boolean function to the set of its upper zeros. Shorter and more transparent proofs for some known properties of \(f\) are presented. The orbits of \(f\) for a direct product of three chains are considered in some detail. Cited in 4 ReviewsCited in 34 Documents MSC: 06A06 Partial orders, general 06E30 Boolean functions Keywords:permutation of antichains; ranked posets; monotone Boolean function; orbits; direct product PDF BibTeX XML Cite \textit{P. J. Cameron} and \textit{D. G. Fon-Der-Flaass}, Eur. J. Comb. 16, No. 6, 545--554 (1995; Zbl 0831.06001) Full Text: DOI OpenURL References: [1] Andrews, G.E, The theory of partitions, () · Zbl 0155.09302 [2] Deza, M; Fukuda, K, Loops of clutter, (), 72-92 [3] Fon-Der-Flaass, D, Orbits of antichains in ranked posets, Europ. J. combin., 14, 17-22, (1993) · Zbl 0777.06002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.