# Shifting Operations and Graded Betti Numbers

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

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## 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

## Copyright information

© Kluwer Academic Publishers 2000