Maximal sized antichains in partial orders

✍ Scribed by D. Kleitman; M. Edelberg; D. Lubell

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 598 KB
• Volume: 1
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(71)90006-9

✦ Synopsis

Abstmt. The following general theorem is proven: Given a partially ordered set and a group Gf prmu tations among itu elements which preserves the order relation, there is a set of elements no twc? c&red acalled an independpnt set, or an antichain) of maximal size which consists of mmplete orbits under the group.

The result is spplicd to several examplco including the lattice of partitions of a set. The maximal size (3f an anticham is also shown to Se the solution of a certain linear program dc fined by the parzial order. Some generalLatio;7s of the main resurult are also described.