  From a combinatorial point of view, we consider the Earth Mover's Distance
(EMD) associated with a metric measure space. The specific case considered is
deceptively simple: Let the finite set [n] = {1,...,n} be regarded as a metric
space by restricting the usual Euclidean distance on the real numbers. The EMD
is defined on ordered pairs of probability distributions on [n]. We provide an
easy method to compute a generating function encoding the values of EMD in its
coefficients, which is related to the Segre embedding from projective algebraic
geometry. As an application we use the generating function to compute the
expected value of EMD in this one-dimensional case. The EMD is then used in
clustering analysis for a specific data set.
