| Home
Research interests
Papers in progress
Published papers
Programming
| Russ Woodroofe - Papers in progress | | | Papers in progress (See also my published papers.) - Russ Woodroofe, Cubical convex ear decompositions. In progress.
On the arXiv Abstract. We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, introduced by Nyman and Swartz, starts with a CL-labeling and uses this to shell the ears of the decomposition. We axiomatize the necessary conditions for this technique as a `CL-ced' or `EL-ced'. We find an EL-ced of the d-divisible partition lattice, and a closely related convex ear decomposition of the coset lattice of a relatively complemented group. Along the way, we construct new EL-labelings of both lattices. The convex ear decompositions so constructed are formed by face lattices of hypercubes.
We then proceed to show that if two posets P1 and P2 have convex ear decompositions (CL-ceds), then their products P1 × P2, P1 \lrtimes P2, and P1 \urtimes P2 also have convex ear decompositions (CL-ceds). An interesting special case is: if P1 and P2 have polytopal order complexes, then so do their products. |