A formula for Plücker coordinates associated with a planar network
| dc.creator | Talaska, Kelli | |
| dc.date | 2008-01-31 | |
| dc.date | 2008-04-15 | |
| dc.date.accessioned | 2026-07-07T10:03:22Z | |
| dc.date.available | 2026-07-07T10:03:22Z | |
| dc.description | For a planar directed graph G, Postnikov's boundary measurement map sends positive weight functions on the edges of G onto the appropriate totally nonnegative Grassmann cell. We establish an explicit formula for Postnikov's map by expressing each Pluecker coordinate as a ratio of two combinatorially defined polynomials in the edge weights, with positive integer coefficients. In the non-planar setting, we show that a similar formula holds for special choices of Pluecker coordinates. | |
| dc.description | 15 pages, 6 figures. Extensive additions, including a generalization for arbitrarily oriented planar graphs and a formula for some Pluecker coordinates of non-planar perfectly oriented graphs | |
| dc.identifier | https://arxiv.org/abs/0801.4822 | |
| dc.identifier | http://arxiv.org/abs/0801.4822 | |
| dc.identifier | Int Math Res Notices (2008) Vol. 2008, article ID rnn081, 19 pages, published on July 24, 2008. | |
| dc.identifier | doi:10.1093/imrn/rnn081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169265 | |
| dc.subject | Combinatorics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A48 (Primary); 05A15 (Secondary) | |
| dc.title | A formula for Plücker coordinates associated with a planar network | |
| dc.type | text |