The median function on distributive semilattices

A median of a k-tuple =(x1; : : : ; xk) of elements of a 0nite metric space (X; d) is an element x for which ∑k i=1 d(x; xi) is minimum. The function m with domain the set of all k-tuples with k ¿ 0 and de0ned by m( ) = {x: x is a median of } is called the median function on X . Continuing with the program of characterizing m on various metric spaces, this paper presents a characterization of the median function on distributive semilattices endowed with the standard lattice metric. ? 2002 Elsevier Science B.V. All rights reserved. MSC: primary 06A12; secondary 05C75