REPRESENTATIONS AND CHARACTERIZATIONS OF VERTICES OF BOUNDED-SHAPE PARTITION POLYTOPES

Consider a finite set whose elements are associated with vectors of co mmon 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 sha re the number of parts) is then the convex hull of the corresponding m atrices. We derive representations and characterizations of these poly topes and their vertices, (C) 1998 Elsevier Science Inc, All rights re served.