Some properties of basic families of subsets

✍ Scribed by Thomas H. Brylawski

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 874 KB
• Volume: 6
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(73)90064-2

✦ Synopsis

A basic system k a nonempty collection of finite incomparable subsets of a set such that for any two subsets or bases in the collection, any flement of one basis can be replaced by some element of the other to give another basis in the collection. In a basic system, any subset of one basis can be bijectively exchanged for distinct ;lements of another; for a fir&~: set, basis complements also have these properties; and certain conditions will guarantee that two such systems on the same set will contain a common basis. All proofs are new, elementary, a2d set-theoretic. In addition, they suggest efficient algorithmic procedures whose efficiencies ar: calculated.