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Let R = k[x_{1},…,x_{n}], where k is a field. Suppose that N is an ideal generated by monomials. We will discuss a construction of Tchernev that approximates the minimal free resolution of R/N using the structure of a finite partially ordered set P. In a previous CRANTS talk we applied this construction to the case when P is the LCM-lattice of N, and used it to describe the minimal free resolution of the class of lattice-linear ideals, which includes among others the class of generic monomial ideals and the class of monomial ideals having linear resolution - two classes very well studied in the literature that until then were not known to have closely related structure. In the present talk we consider another extremely well studied and also seemingly unrelated class of ideals - the class of stable ideals - and explain how their minimal free resolutions can also be obtained by using our construction. In this case the poset P can be taken to be the poset of so-called Eliahou-Kervaire admissible symbols. Along the way we also obtain some surprisingly nice topological and combinatorial properties of this poset.
Refreshments at 3:45 pm in ES 152