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Homological shifts of polymatroidal ideals

Commutative Algebra 2025-01-15 v3

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.

Keywords

Cite

@article{arxiv.2205.04163,
  title  = {Homological shifts of polymatroidal ideals},
  author = {Antonino Ficarra},
  journal= {arXiv preprint arXiv:2205.04163},
  year   = {2025}
}

Comments

This is the final version of the paper, accepted for publication in Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie