MONOTONE OPTIMAL MULTIPARTITIONS USING SCHUR CONVEXITY WITH RESPECT TO PARTIAL ORDERS

In a (t, n, m)-multipartitioning problem, t lists of mm ordered number are partitioned into n sets. where each set contains m numbers from e ach list. The goal is to maximize some objective function that depends on the sum of the elements in each set and is called the partition fu nction. The authors use the recently developed theory of majorization and Schur convexity with respect to partially ordered sets to study op timal multipartitions for the above problem. In particular, they apply the results to construct a class of counterexamples to a recent conje cture of Du and Hwang, which asserts that (classic) Schur convex funct ions can be characterized as the partition functions for (1, n, m)-mul tipartitioning problems having monotone optimal solutions.