Restricted lattice paths and the cd-index of a product

A butterfly poset is the face poset of a regular subdivision of a sphere with two cells in each dimension. The cd-index of a diamond product of such posets has coefficients which can be interpreted as counting lattice paths satisfying a certain restriction. We show how this interpretation arises naturally from the coalgebraic point of view. We will also prove a unimodality result on the coefficients of such a product with fixed total rank. This reports on joint work with Richard Ehrenborg.