Title
Singular Points and an Upper Bound of Medians in Upper Semimodular Lattices
Document Type
Article
Publication Date
9-28-2000
Abstract
Given a k-tuple P=(x 1,x 2,...,x k ) in a finite lattice X endowed with the lattice metric d, a median of P is an element m of X minimizing the sum ∑ i d(m,x i ). If X is an upper semimodular lattice, Leclerc proved that a lower bound of the medians is c(P), the majority rule and he pointed out an open problem: “Is c 1(P)=∨ i x i , the upper bound of the medians?” This paper shows that the upper bound is not c 1(P) and gives the best possible upper bound.
Recommended Citation
Li, Jinlu and Boukaabar, Kaddour, "Singular Points and an Upper Bound of Medians in Upper Semimodular Lattices" (2000). Faculty Emeritus. 15.
https://digitalcommons.shawnee.edu/fac_emeritus/15
