An extremal problem for antichains of subsets of a multiset

✍ Scribed by G.F. Clements

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 850 KB
• Volume: 63
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(87)90146-4

✦ Synopsis

A multiset M is a finite set consisting of several different kinds of elements, and an antichain F is a set of incomparable subsets of M. With P and _F denoting respectively the set of subsets which contain an element of F or are contained in an element of F, we find the best upper bound for min(lFI, IFI), thus generalizing a result of D.E. Daykin [9] for ordinary sets.

Extremal antichains are partially characterized.