Generic 3-connected planar constraint systems are not soluble by radicals
| dc.creator | Owen, John C. | |
| dc.creator | Power, Stephen C. | |
| dc.date | 2003-11-04 | |
| dc.date.accessioned | 2026-07-07T05:02:35Z | |
| dc.date.available | 2026-07-07T05:02:35Z | |
| dc.description | We show that planar embeddable 3-connected CAD graphs are generically non-soluble. A CAD graph represents a configuration of points on the Euclidean plane with just enough distance dimensions between them to ensure rigidity. Formally, a CAD graph is a maximally independent graph, that is, one that satisfies the vertex-edge count 2v - 3 = e together with a corresponding inequality for each subgraph. The following main theorem of the paper resolves a conjecture of Owen in the planar case. Let G be a maximally independent 3-connected planar graph, with more than 3 vertices, together with a realisable assignment of generic dimensions for the edges which includes a normalised unit length (base) edge. Then, for any solution configuration for these dimensions on a plane, with the base edge vertices placed at rational points, not all coordinates of the vertices lie in a radical extension of the dimension field. | |
| dc.description | 45 pages, 11 figures | |
| dc.identifier | https://arxiv.org/abs/math/0311037 | |
| dc.identifier | http://arxiv.org/abs/math/0311037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69062 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 68U07, 12F10, 05C40 (primary), 52C25, 13P99 (secondary) | |
| dc.title | Generic 3-connected planar constraint systems are not soluble by radicals | |
| dc.type | text |