Computation of graded ideals with given extremal Betti numbers in a polynomial ring

DOI10.1016/j.jsc.2018.04.019zbMath1441.13023OpenAlexW2800425762WikidataQ129953611 ScholiaQ129953611MaRDI QIDQ1733305

Marilena Crupi, Luca Amata

Publication date: 21 March 2019

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2018.04.019

zbMATH Keywords

algorithmsextremal Betti numbersmonomial idealsgraded idealsminimal graded resolution

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Computational aspects and applications of commutative rings (13P99) Polynomials over commutative rings (13B25) Syzygies, resolutions, complexes and commutative rings (13D02) Graded rings and modules (associative rings and algebras) (16W50)

Related Items (4)

A numerical characterization of the extremal Betti numbers of \(t\)-spread strongly stable ideals ⋮ Computing general strongly stable modules with given extremal Betti numbers ⋮ ON THE EXTREMAL BETTI NUMBERS OF SQUAREFREE MONOMIAL IDEALS ⋮ Projective dimension and Castelnuovo–Mumford regularity of t-spread ideals

Uses Software

• CoCoA
• CoCoALib
• Macaulay2

Cites Work

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• Minimal resolutions of some monomial submodules
• Extremal Betti numbers of graded modules
• Minimal resolutions of some monomial ideals
• Extremal Betti numbers of graded ideals
• Extremal Betti numbers and applications to monomial ideals
• Hilbert functions of \(d\)-regular ideals
• Piecewise lexsegment ideals
• The possible extremal Betti numbers of a homogeneous ideal

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