The Positive Bergman Complex of an Oriented Matroid
| dc.creator | Ardila, Federico | |
| dc.creator | Klivans, Caroline | |
| dc.creator | Williams, Lauren | |
| dc.date | 2004-06-07 | |
| dc.date.accessioned | 2026-07-07T05:08:57Z | |
| dc.date.available | 2026-07-07T05:08:57Z | |
| dc.description | We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive Bergman complex is defined so that given a linear ideal I with associated oriented matroid M_I, the positive tropical variety associated to I is equal to the fan over B+(M_I). Our main result is that a certain "fine" subdivision of B+(M) is a geometric realization of the order complex of the proper part of the Las Vergnas face lattice of M. It follows that B+(M) is homeomorphic to a sphere. For the oriented matroid of the complete graph K_n, we show that the face poset of the "coarse" subdivision of B+(K_n) is dual to the face poset of the associahedron A_{n-2}, and we give a formula for the number of fine cells within a coarse cell. | |
| dc.description | 15 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0406116 | |
| dc.identifier | http://arxiv.org/abs/math/0406116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71461 | |
| dc.subject | Combinatorics | |
| dc.title | The Positive Bergman Complex of an Oriented Matroid | |
| dc.type | text |