Edgewise Cohen-Macaulay connectivity of partially ordered sets - Athanasiadis, Christos A.; Kallipoliti, Myrto (MATHEMATICA SCANDINAVICA, 2018)
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.