2022/05/09 by Ficarra, Antonino · 3 citations
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2205.04163
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.