Algorithms for strongly stable ideals

Details Algorithms for strongly stable ideals Algorithms for strongly stable ideals

2011-10-18

arxiv.org/abs/1110.4080v2

Mathematics

Commutative Algebra

22 pages, reference added, proposition removed, table modified

Scientific paper

Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ideals with a given Hilbert polynomial, in this note we present three algorithms to produce all strongly stable ideals with certain prescribed properties: the saturated strongly stable ideals with a given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert polynomial, and the saturated strongly stable ideals with a given Hilbert function. We also establish results for estimating the complexity of our algorithms.

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