Algorithms for strongly stable ideals
Commutative Algebra
2011-12-05 v2 Algebraic Geometry
Combinatorics
Abstract
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.
Cite
@article{arxiv.1110.4080,
title = {Algorithms for strongly stable ideals},
author = {Dennis Moore and Uwe Nagel},
journal= {arXiv preprint arXiv:1110.4080},
year = {2011}
}
Comments
22 pages, reference added, proposition removed, table modified