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Homological Shift Ideals: Macaulay2 Package

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arxiv 2309.09271 v1 pith:TS5IKB4R submitted 2023-09-17 math.AC math.CO

Antonino Ficarra This is my paper · ORCID
classification math.ACmath.CO
keywords homologicalpackageshifthavingidealslinearmacaulay2allows
verification ladder T0 review T1 audit T2 compute T3 formal

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We introduce the Macaulay2 package HomologicalShiftIdeals. It allows to compute the homological shift ideals of a monomial ideal, and to check the homological shift properties, including having linear resolution, having linear quotients, or being polymatroidal. The theory behind these concepts is explained and the main features of the package are presented.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Powers of Edge Ideals with Linear Quotients

    math.AC 2024-12 accept novelty 8.0 of 10

    Explicit linear quotient orderings exist for all powers of anticycle edge ideals and for powers of any quadratic monomial ideal with linear quotients.

  2. Principal vector-spread Borel ideals

    math.AC 2025-07 conditional novelty 7.0 of 10

    For squarefree principal vector-spread Borel ideals, the paper gives the minimal primary decomposition, proves sequential Cohen-Macaulayness, and classifies normal torsionfreeness via the index bounds j_i <= sum_{s<=i} t_s.

  3. The homological shift algebra of a monomial ideal

    math.AC 2024-12 conditional novelty 7.0 of 10

    For monomial ideals with linear powers, the homological shift algebra is a finitely generated Rees module, making regularity, depth, associated primes, v-number, and Golodness of homological shift ideals eventually li...

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