Symmetric iterated Betti numbers
| dc.creator | Babson, Eric | |
| dc.creator | Novik, Isabella | |
| dc.creator | Thomas, Rekha | |
| dc.date | 2002-06-07 | |
| dc.date.accessioned | 2026-07-07T04:48:56Z | |
| dc.date.available | 2026-07-07T04:48:56Z | |
| dc.description | We define a set of invariants of a homogeneous ideal $I$ in a polynomial ring called the symmetric iterated Betti numbers of $I$. For $I_Γ$, the Stanley-Reisner ideal of a simplicial complex $Γ$, these numbers are the symmetric counterparts of the exterior iterated Betti numbers of $Γ$ introduced by Duval and Rose. We show that the symmetric iterated Betti numbers of an ideal $I$ coincide with those of a particular reverse lexicographic generic initial ideal $\Gin(I)$ of $I$, and interpret these invariants in terms of the associated primes and standard pairs of $\Gin(I)$. We verify that for an ideal $I=I_Γ$ the extremal Betti numbers of $I_Γ$ are precisely the extremal (symmetric or exterior) iterated Betti numbers of $Γ$. We close with some results and conjectures about the relationship between symmetric and exterior iterated Betti numbers of a simplicial complex. | |
| dc.description | 20 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0206063 | |
| dc.identifier | http://arxiv.org/abs/math/0206063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64242 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 05E02;13A02 | |
| dc.title | Symmetric iterated Betti numbers | |
| dc.type | text |