English

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.

Keywords

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

R2 v1 2026-06-21T19:22:20.122Z