
TL;DR
This paper introduces weighted Borel generators, a refined subset of generators for a special class of monomial ideals called strongly stable ideals, enabling more efficient algebraic computations.
Contribution
It defines weighted Borel generators for w-stable ideals and provides a Macaulay2 package for their computation, extending prior formulas for Hilbert series and Betti numbers.
Findings
Defined weighted Borel generators for w-stable ideals
Developed a Macaulay2 package for computations
Extended formulas for Hilbert series and Betti numbers
Abstract
Strongly stable ideals are a class of monomial ideals which correspond to generic initial ideals in characteristic zero and can be described completely by their Borel generators, a subset of the minimal monomial generators of the ideal. Francisco, Mermin, and Schweig developed formulas for the Hilbert series and Betti numbers of strongly stable ideals in terms of their Borel generators. In this work, a specialization of strongly stable ideals is presented which further restricts the subset of relevant generators. A choice of weight vector restricts the set of strongly stable ideals to a subset designated as -stable ideals. This restriction further compresses the Borel generators to a subset termed the weighted Borel generators of the ideal. A new Macaulay2 package wStableIdeals.m2 has been developed alongside this paper and segments of code support…
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.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Stochastic processes and financial applications · Mathematical and Theoretical Analysis
