The Frechet Contingency Array Problem is Max-Plus Linear

In this paper we show that the so-called array Frechet problem in Probability/Statistics is (max,+)-linear. The upper bound of Frechet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Frechet problem and the Monge property of bivariate distribution.