Cubical convex ear decompositions

Details Cubical convex ear decompositions Cubical convex ear decompositions

2007-09-18

arxiv.org/abs/0709.2793v3

Electronic J. Combinatorics 16(2) (2009) R17

Mathematics

Combinatorics

33 pages. v2 shows that products of spaces with ceds have ceds (which was a question in v1), improves exposition. v3 further i

Scientific paper

We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, first used 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 P_1 and P_2 have convex ear decompositions (CL-ceds), then their products P_1 \times P_2, P_1 \lrtimes P_2, and P_1 \urtimes P_2 also have convex ear decompositions (CL-ceds). An interesting special case is: if P_1 and P_2 have polytopal order complexes, then so do their products.

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