Edgewise Cohen-Macaulay connectivity of partially ordered sets
arXiv:1504.04062
Abstract
The proper parts of face lattices of convex polytopes are shown to satisfy a strong form of the Cohen--Macaulay property, namely that removing from their Hasse diagram all edges in any closed interval results in a Cohen--Macaulay poset of the same rank. A corresponding notion of edgewise Cohen--Macaulay connectivity for partially ordered sets is investigated. Examples and open questions are discussed.
Major revision, 11 pages, 3 figures