Orbits of Antichains in Ranked Posets

✍ Scribed by D.G. Fon-Der-Flaass

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 149 KB
• Volume: 14
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1993.1003

✦ Synopsis

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. For (P) a direct product of two chains, possible lengths of orbits are completely determined.