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Multigraded Betti numbers without computing minimal free resolutions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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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Authors and Affiliations

  1. Universidad de La Rioja, Lagroño, La Rioja, Spain

    Eduardo Sáenz-de-Cabezón

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  1. Eduardo Sáenz-de-Cabezón
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Correspondence to Eduardo Sáenz-de-Cabezón.

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Sáenz-de-Cabezón, E. Multigraded Betti numbers without computing minimal free resolutions. AAECC 20, 481–495 (2009). https://doi.org/10.1007/s00200-009-0112-6

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  • DOI: https://doi.org/10.1007/s00200-009-0112-6

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