Multigraded betti numbers without computing minimal free resolutions

  1. Sáenz-De-Cabezón, E. 1
  1. 1 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Applicable Algebra in Engineering, Communications and Computing

ISSN: 0938-1279

Year of publication: 2009

Volume: 20

Issue: 5

Pages: 481-495

Type: Article

Export: RIS
DOI: 10.1007/s00200-009-0112-6 SCOPUS: 2-s2.0-73449141769 WoS: 000272118300008
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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. © 2009 Springer-Verlag.