Monomial Bases for Broken Circuit Complexes
| dc.creator | Brown, Jason | |
| dc.creator | Sagan, Bruce | |
| dc.date | 2006-01-25 | |
| dc.date.accessioned | 2026-07-07T06:59:18Z | |
| dc.date.available | 2026-07-07T06:59:18Z | |
| dc.description | Let F be a field and let G be a finite graph with a total ordering on its edge set. Richard Stanley noted that the Stanley-Reisner ring F(G) of the broken circuit complex of G is Cohen-Macaulay. Jason Brown gave an explicit description of a homogeneous system of parameters for F(G) in terms of fundamental cocircuits in G. So F(G) modulo this hsop is a finite dimensional vector space. We conjecture an explicit monomial basis for this vector space in terms of the circuits of G and prove that the conjecture is true for two infinite families of graphs. We also explore an application of these ideas to bounding the number of acyclic orientations of G from above. | |
| dc.identifier | https://arxiv.org/abs/math/0601619 | |
| dc.identifier | http://arxiv.org/abs/math/0601619 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107697 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 05E99; Secondary 05C99, 13A02 | |
| dc.title | Monomial Bases for Broken Circuit Complexes | |
| dc.type | text |