Introduction. Consider the problem of partitioning a set N of n distinct
numbers into nonempty disjoint parts. The partition is called an open-partition if the
number of parts is not prespecified and called a p-partition if the number is specified
to be p If, furthermore a set {nl np} with P
-.=1 n n is prespecified to be the
set of sizes of the p parts, then the partition is called a shape-partition, shape referring
to the set {ni}