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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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