The median function on Boolean lattices

Abstract

A median of a sequence π = ( x1, x2, …, xk) of elements of a finite metric space (X, d) is an element x ∈ X for which [Formula: see text] is a minimum. The function Median with domain the set of all finite sequences on X and defined by Med (π) = {x : x is a median of π} is called the median function on X. In this paper, the median function on finite Boolean lattices is axiomatically characterized via location functions.