The moduli space of n tropically collinear points in R^d
| dc.creator | Develin, Mike | |
| dc.date | 2004-01-19 | |
| dc.date | 2004-10-22 | |
| dc.date.accessioned | 2026-07-07T05:04:38Z | |
| dc.date.available | 2026-07-07T05:04:38Z | |
| dc.description | The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of d by n matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension d=3 and compute its homology in this case, conjecturing that this complex is shellable in general. We also investigate the space of d by n matrices of Barvinok rank two, a subcomplex directly related to optimization, giving a complete description of this subcomplex in the case d=3. | |
| dc.description | 16 pages; revised version to appear in Collectanea Mathematica | |
| dc.identifier | https://arxiv.org/abs/math/0401224 | |
| dc.identifier | http://arxiv.org/abs/math/0401224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69885 | |
| dc.subject | Combinatorics | |
| dc.subject | 52B05;57Q05 | |
| dc.title | The moduli space of n tropically collinear points in R^d | |
| dc.type | text |