Abstract
We use Mayer-Vietoris trees to obtain the multigraded Betti numbers of monomial ideals without computing their minimal free resolutions. This method provides not only a competitive algorithm for such computations but also a new tool for the analysis of the homological structure of monomial ideals. Using Mayer-Vietoris trees we obtain new results for several families of monomial ideals and new proofs of known results for other families.
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