Journal of Algebraic Combinatorics

, Volume 12, Issue 3, pp 207–222

Shifting Operations and Graded Betti Numbers

Authors

  • Annetta Aramova
  • Jürgen Herzog
  • Takayuki Hibi
Article

DOI: 10.1023/A:1011238406374

Cite this article as:
Aramova, A., Herzog, J. & Hibi, T. Journal of Algebraic Combinatorics (2000) 12: 207. doi:10.1023/A:1011238406374

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 shiftingshifted complexesgeneric initial idealsextremal Betti numbers
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© Kluwer Academic Publishers 2000