Algorithms for strongly stable ideals

Dennis Moore, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 paper 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.

Original languageEnglish
Pages (from-to)2527-2552
Number of pages26
JournalMathematics of Computation
Volume83
Issue number289
DOIs
StatePublished - 2014

Keywords

  • Betti numbers
  • Castelnuovo-Mumford regularity
  • Hilbert polynomial
  • Lexsegment ideal
  • Strongly stable ideal

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Algorithms for strongly stable ideals'. Together they form a unique fingerprint.

Cite this