A median of a k-tuple π=(x 1,...,x k) of elements of a finite metric space (X,d) is an element x for which ∑ i=1 kd(x,x i) is minimum. The function m with domain the set of all k-tuples with k0 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.

Consensus, Distributive semilattice, Median function
dx.doi.org/10.1016/S0166-218X(02)00213-5, hdl.handle.net/1765/66679
Discrete Applied Mathematics
Erasmus School of Economics

McMorris, F.R, Mulder, H.M, & Powers, R.C. (2003). The median function on distributive semilattices. In Discrete Applied Mathematics (Vol. 127, pp. 319–324). doi:10.1016/S0166-218X(02)00213-5