منابع مشابه
Reverse search for monomial ideals
We give a set of multidegrees that support all the numerical information for a monomial ideal that can be reverse searched and hence is parallelizable and has space complexity that is polynomial in the size of the input. Our approach uses a new definition of closed sets for simplicial complexes that may be useful in other contexts.
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Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geometry.
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These are lecture notes, in progress, on monomial ideals. The point of view is that monomial ideals are best understood by drawing them and looking at their corners, and that a combinatorial duality satisfied by these corners, Alexander duality, is key to understanding the more algebraic duality theories at play in algebraic geometry and commutative algebra. Sections written so far cover Alexan...
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We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire’s splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bi...
متن کاملRigid monomial ideals
In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the m...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2009
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2009.05.002