Journal of Algebraic Combinatorics

, Volume 12, Issue 3, pp 207–222 | Cite as

Shifting Operations and Graded Betti Numbers

  • Annetta Aramova
  • Jürgen Herzog
  • Takayuki Hibi
Article

Abstract

The behaviour of graded Betti numbers under exterior and symmetric algebraic shifting is studied. It is shown that the extremal Betti numbers are stable under these operations. Moreover, the possible sequences of super extremal Betti numbers for a graded ideal with given Hilbert function are characterized. Finally it is shown that over a field of characteristic 0, the graded Betti numbers of a squarefree monomial ideal are bounded by those of the corresponding squarefree lexsegment ideal.

algebraic shifting shifted complexes generic initial ideals extremal Betti numbers 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Annetta Aramova
  • Jürgen Herzog
  • Takayuki Hibi

There are no affiliations available

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