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arXiv · 2310.14247

A quasi-additive property of homological shift ideals

Shamila Bayati
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Abstract

In this paper, we investigate which classes of monomial ideals have a quasi-additive property of homological shift ideals. More precisely, for a monomial ideal $I$ we are interested to find out whether $HS_{i+j}(I)\subseteq HS_i(HS_j(I))$. It turns out that $\mathbf{c}$-bounded principal Borel ideals as well as polymatroidal ideals satisfying strong exchange property, and polymatroidal ideals generated in degree two have this quasi-additive property. For squarefree Borel ideals, we even have equality. Besides, the inclusion holds for every equigenerated Borel ideal and polymatroidal ideal when $j=1$.

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Shamila Bayati. 2023-10-22. A quasi-additive property of homological shift ideals. https://doi.org/10.1007/s40840-023-01506-1

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