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Homological shifts of polymatroidal ideals

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arxiv 2205.04163 v3 pith:VHXSDK5I submitted 2022-05-09 math.AC

Antonino Ficarra This is my paper · ORCID
classification math.AC
keywords polymatroidalhomologicalidealidealsbayaticonjectureshiftshifts
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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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Cited by 2 Pith papers

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

  1. On the homological shifts of cover ideals of Cohen-Macaulay graphs

    math.AC 2025-06 conditional novelty 8.0 of 10

    For every k≥2, a Cohen-Macaulay very well-covered whiskered bipartite graph has non-linear HS_k, and the paper identifies classes where HS_k does have linear quotients.

  2. Syzygies of polymatroidal ideals

    math.AC 2025-07 conditional novelty 7.0 of 10

    For every polymatroid, the cave polynomial is valuative, its support is a generalized polymatroid, and its coefficients are the Möbius values, settling the Bandari-Bayati-Herzog and Castillo-Cid-Ruiz-Mohammadi-Montano...

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