# Shellability of Exponentional Structures

Abstract. Let \Pi(d)n denote the set of partitions of nd whose blocks are divisible by d, let \Pin,r denote the set of vector partitions of the Cartesian product of r copies of n, and let \chin denote the set of colored graphs on a vertex set of n elements. Each of these sets has a natural partial ordering. We show that each of these partially ordered sets is shellable, using the notion of recursive atom orderings.

The paper has been finally published under the same title in Order 3 (1986), 47-54.