In this paper we discuss the characterization problem
for posets of interval dimension at most 2. That is, we
attempt to compile the minimal list of forbidden posets
for interval dimension 2. Members of this list are
called 3-interval irreducible posets. The problem is
related to a series of characterization problems which
have been solved earlier. These are: The
characterization of planar lattices, due to Kelly and
Rival, the characterization of posets of dimension at
most 2 (3-irreducible posets) which has been obtained
independently by Trotter and Moore and by Kelly and the
characterization of bipartite 3-interval irreducible
posets due to Trotter. We show that every 3-interval
irreducible poset is a reduced partial stack of some
bipartite 3-interval irreducible poset. Moreover, we
succeed in classifying the 3-interval irreducible
partial stacks of most of the bipartite 3-interval
irreducible posets. Our arguments depend on a
transformation P o B(P), such that `dim: P =
dim: B(P)`. This transformation has been introduced
by Felsner, Habib and Möhring
(see Report-285-1991}).
