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arXiv · 2205.04163

Homological shifts of polymatroidal ideals

Antonino Ficarra
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Abstract

We study the homological shifts of polymatroidal ideals. In our main theorem we prove that the first homological shift ideal of any polymatroidal ideal is again polymatroidal, supporting a conjecture of Bandari, Bayati and Herzog that predicts that all homological shift ideals of a polymatroidal ideal are polymatroidal. As a nice consequence, we recover a result of Bayati which proves this conjecture in the squarefree case.

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Antonino Ficarra. 2022-05-09. Homological shifts of polymatroidal ideals. https://arxiv.org/abs/2205.04163

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