The median function on Boolean lattices

摘要

A median of a sequence π = （x_, x_2,..., x_k) of elements of a finite metric space (X, d) is an element x ∈ X for which ∑_(i=1)~k d(x, x_i) 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.