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Consecutive cancellations in Betti numbers. (English) Zbl 1099.13505
Summary: Let $$I$$ be a homogeneous ideal in a polynomial ring over a field. By Macaulay’s theorem, there exists a lexicographic ideal $$L$$ with the same Hilbert function as $$I$$. We prove that the graded Betti numbers of $$I$$ are obtained from those of $$L$$ by a sequence of consecutive cancellations.

##### MSC:
 13D02 Syzygies, resolutions, complexes and commutative rings
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