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.
Homological Shift Ideals: Macaulay2 Package
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abstract
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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Principal vector-spread Borel ideals
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.