Orbits of antichains revisited. (English) Zbl 0831.06001

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.


06A06 Partial orders, general
06E30 Boolean functions
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[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
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