Alexander duality is made into a functor which extends the notion for monomial ideals to any finitely generated N-graded module. The functors associated with Alexander duality provide a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries. A minimal injective resolution of a module M is equivalent to the injective resolution ...

Let A be a semigroup whose only invertible element is 0. For an A-homogeneous ideal we discuss the notions of simple i-syzygies and simple minimal free resolutions of R/I. When I is a lattice ideal, the simple 0-syzygies of R/I are the binomials in I. We show that for an appropriate choice of bases every A-homogeneous minimal free resolution of R/I is simple. We introduce the gcd-complex ∆gcd(b...

Some anaphora resolution algorithms are based on model builders, and use the fact that they generate minimal models: only those elements that are necessary are postulated to exist in the model. In this way, such systems have the desirable property that if anaphora can be resolved to a linguistically available antecedent, this resolution applies, and only if there is no suitable antecedent, a de...

The minimal free resolution of the Jacobian ideals of the determinant polynomial were computed by Lascoux [12], and it is an active area of research to understand the Jacobian ideals of the permanent, see e.g., [13, 9]. As a step in this direction we compute several new cases and completely determine the linear strands of the minimal free resolutions of the ideals generated by sub-permanents. O...

The minimal free resolution of the coordinate ring a complete intersection in projective space is Koszul complex on regular sequence. In product spaces P1×P1, we investigate which sets points have virtual that This paper provides conditions points; some guarantee this property, and do not property.

We introduce a robust statistical approach to realization from Minimal Recursion Semantics representations. The approach treats realization as a translation problem, transforming the Dependency MRS graph representation to a surface string. Translation is based on a Synchronous Context-Free Grammar that is automatically extracted from a large corpus of parsed sentences. We have evaluated the new...

We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this shows that thresh...