Current browse context:
math.AC
Change to browse by:
References & Citations
Mathematics > Commutative Algebra
Title: Matching powers of monomial ideals and edge ideals of weighted oriented graphs
(Submitted on 24 Sep 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We introduce the concept of matching powers of monomial ideals. Let $I$ be a monomial ideal of $S=K[x_1,\dots,x_n]$, with $K$ a field. The $k$th matching power of $I$ is the monomial ideal $I^{[k]}$ generated by the products $u_1\cdots u_k$ where $u_1,\dots,u_k$ is a monomial regular sequence contained in $I$. This concept naturally generalizes that of squarefree powers of squarefree monomial ideals. We study depth and regularity functions of matching powers of monomial ideals and edge ideals of weighted oriented graphs. We show that the last nonvanishing power of a quadratic monomial ideal is always polymatroidal and thus has a linear resolution. When $I$ is a non-quadratic edge ideal of a weighted oriented forest, we characterize when $I^{[k]}$ has a linear resolution.
Submission history
From: Antonino Ficarra [view email][v1] Sun, 24 Sep 2023 22:53:46 GMT (25kb)
[v2] Wed, 27 Mar 2024 09:07:36 GMT (25kb)
Link back to: arXiv, form interface, contact.