The median function on distributive semilattices

AbstractA median of a k-tuple π=(x1,…,xk) of elements of a finite metric space (X,d) is an element x for which ∑i=1kd(x,xi) is minimum. The function m with domain the set of all k-tuples with k>0 and defined by m(π)={x:x is a median of π} 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