Weighted Borel Generators
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912002507538432 |
|---|---|
| author | Ireland, Seth |
| author_facet | Ireland, Seth |
| contents | 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 $w\in\mathbb{N}_{> 0}^n$ restricts the set of strongly stable ideals to a subset designated as $w$-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 computations within. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Borel Generators Ireland, Seth Commutative Algebra Combinatorics 13D02, 13D40, 05E40 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 $w\in\mathbb{N}_{> 0}^n$ restricts the set of strongly stable ideals to a subset designated as $w$-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 computations within. |
| title | Weighted Borel Generators |
| topic | Commutative Algebra Combinatorics 13D02, 13D40, 05E40 |
| url | https://arxiv.org/abs/2408.04120 |