Lattice valuations, medians and majorities

✍ Scribed by Bruno Leclerc

• Book ID: 103056930
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 793 KB
• Volume: 111
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90169-t

✦ Synopsis

Medians in a finite semilattice endowed with a metric of a classical type are considered. First, upper valuations and their associated metrics are characterized by the fact that the majority rule provides a lower bound for the medians. The set of all the medians is more precisely described in the case of a lower-distributive semilattice endowed with a generalized valuation.

Rtsumh

Leclerc, B., Lattice valuations, medians and majorities, Discrete Mathematics 111 (1993) 345-356. On etudie les medianes dans un demi-treillis fini muni dune distance dun type classique. On caracti'rise d'abord les valuations superieures, et leurs mttriques associees, par le fait que la regle majoritaire fournit une borne inferieure pour les medianes. On decrit plus prkisement l'ensemble des medianes dans le cas dun demi-treillis inferieurement distributif muni d'une valuation generahste.