From the abstract: We give a brief survey of the various topological and combinatorial techniques which have been used to construct the minimal free resolution of a stable monomial ideal in a polynomial ring over a field. The new results appearing in this paper describe a connection between certain topological and combinatorial methods for the description of said minimal resolutions. In particular, we construct a minimal poset resolution of an arbitrary stable monomial ideal by using a poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. (…) We exhibit a regular CW-complex which supports this resolution.
For the entire collection see [Zbl 1237.13005].