On sequentially Cohen-Macaulay posets

Several different types of algebras that we are interested in are Koszul if and only if certain associated posets have all their open intervals Cohen-Macaulay. When we relax the latter to being sequentially Cohen-Macaulay, a certain deformation of the initial algebra becomes Koszul. We will present combinatorially inspired examples of such occurrences and describe the interplay between combinatorics and algebra facilitating the situation. This is joint work with Vic Reiner.