Representations and characterizations of vertices of bounded-shape partition polytopes

Abstract

Consider a finite set whose elements are associated with vectors of common dimension. A partition of such a set is associated with a matrix whose columns are the sums of the vectors corresponding to each part. The partition polytope associated with a class of partitions (that share the number of parts) is then the convex hull of the corresponding matrices. We derive representations and characterizations of these polytopes and their vertices, (C) 1998 Elsevier Science Inc, All rights reserved.