Monomial ideals with regular quotients and some edge rings
Dancheng Lu, Hao Zhou
TL;DR
This paper introduces monomial ideals with regular quotients, extending linear quotients, and uses this framework to compute Betti numbers of toric ideals in various edge rings.
Contribution
It extends the concept of monomial ideals with linear quotients to regular quotients and applies this to calculate Betti numbers of toric ideals in edge rings.
Findings
Calculated Betti numbers for classes of edge rings
Extended linear quotient concepts to regular quotients
Provided new methods for analyzing monomial ideals
Abstract
We introduce and study monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging to various classes of edge rings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation