Shifting Operations and Graded Betti Numbers
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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.
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- Shifting Operations and Graded Betti Numbers
Journal of Algebraic Combinatorics
Volume 12, Issue 3 , pp 207-222
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- Kluwer Academic Publishers
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- algebraic shifting
- shifted complexes
- generic initial ideals
- extremal Betti numbers