This paper investigates a transformation P o Q
between partial orders P,Q that transforms the
interval dimension of P to the dimension of Q,
i.e. sl Idim(P) = sl dim(Q). Such a construction
has been shown before in the context of Ferrer's
dimension by Cogis. Our construction can be shown to be
equivalent to his, but it has the advantage of (1)
being purely order-theoretic, (2) providing a geometric
interpretation of interval dimension similar to that of
Ore for dimension, and (3) revealing several somewhat
surprising connections to other order-theoretic
results. For instance, the transformation P o Q can
be seen as an almost inverse of the well-known split
operation, it provides a theoretical background for the
influence of edge subdivision on dimension (e.g. the
results of Spinrad) and interval dimension, and it
turns out to be invariant with respect to changes of
P that do not alter its comparability graph, thus
providing also a simple new proof for the comparability
invariance of interval dimension.
