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