Abstract
We study the problem of determining when the lexicographic sum ? q?Q P q of a family of posets {P q/q?Q} over a posetQ is Cohen-Macaulay or shellable. Our main result, a characterization of when the lexicographic sum is Cohen-Macaulay, is proven using combinatorial methods introduced by Garsia. A similar characterization for when the lexicographic sum is CL (chainwise-lexicographically)-shellable, is derived using the recursive atom ordering method due to Bjorner and Wachs.
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