Powers of Edge Ideals with Linear Quotients
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909651669352448 |
|---|---|
| author | Basser, Etan Diethorn, Rachel Miranda, Robert Stinson-Maas, Mario |
| author_facet | Basser, Etan Diethorn, Rachel Miranda, Robert Stinson-Maas, Mario |
| contents | We prove that second and higher powers of the edge ideals of anticycles admit linear quotient orderings, although the edge ideals themselves do not, thus resolving an open question of Hoefel and Whieldon in the affirmative and providing the first class of gap-free graphs whose edge ideals satisfy this property on their powers. We also construct an explicit and straightforward linear quotient ordering for any power of a quadratic monomial ideal which admits linear quotients. This expands on a well-known result of Herzog, Hibi, and Zheng. As a consequence, we give explicit formulas for the projective dimension and Betti numbers of the edge ideals of whisker graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03468 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Powers of Edge Ideals with Linear Quotients Basser, Etan Diethorn, Rachel Miranda, Robert Stinson-Maas, Mario Commutative Algebra 13D02, 13F55, 13P20, 05E40 We prove that second and higher powers of the edge ideals of anticycles admit linear quotient orderings, although the edge ideals themselves do not, thus resolving an open question of Hoefel and Whieldon in the affirmative and providing the first class of gap-free graphs whose edge ideals satisfy this property on their powers. We also construct an explicit and straightforward linear quotient ordering for any power of a quadratic monomial ideal which admits linear quotients. This expands on a well-known result of Herzog, Hibi, and Zheng. As a consequence, we give explicit formulas for the projective dimension and Betti numbers of the edge ideals of whisker graphs. |
| title | Powers of Edge Ideals with Linear Quotients |
| topic | Commutative Algebra 13D02, 13F55, 13P20, 05E40 |
| url | https://arxiv.org/abs/2412.03468 |