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{\bf Russ Woodroofe}
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{\bf Cubical Convex Ear Decompositions}
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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
finite 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 $P_{1}\times P_{2}$,
$P_{1}\check{\times} P_{2}$, and $P_{1}\hat{\times} P_{2}$ 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. 

\bye