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 language | English |
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Pages (from-to) | 2527-2552 |
Number of pages | 26 |
Journal | Mathematics of Computation |
Volume | 83 |
Issue number | 289 |
DOIs | |
State | Published - 2014 |
Bibliographical note
Publisher Copyright:© 2014 American Mathematical Society.
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