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Séminaire Lotharingien de Combinatoire, B10f (1984).

[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 244/S-110, p.
107-116.]

# Bruce E. Sagan

# Shellability of Exponentional Structures

**Abstract.**
Let *\Pi*^{(d)}_{n}
denote the set of partitions of *nd* whose
blocks are divisible by *d*, let
*\Pi*_{n,r} denote the set
of vector partitions
of the Cartesian product of *r* copies of *n*, and let
*\chi*_{n}
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.