Lower bounds for simplicial covers and triangulations of cubes
| dc.creator | Bliss, Adam | |
| dc.creator | Su, Francis Edward | |
| dc.date | 2003-10-10 | |
| dc.date.accessioned | 2026-07-07T06:33:36Z | |
| dc.date.available | 2026-07-07T06:33:36Z | |
| dc.description | We show that the size of a minimal simplicial cover of a polytope $P$ is a lower bound for the size of a minimal triangulation of $P$, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their exterior faces. | |
| dc.description | 17 pages, related work at http://www.math.hmc.edu/~su/papers.html | |
| dc.identifier | https://arxiv.org/abs/math/0310142 | |
| dc.identifier | http://arxiv.org/abs/math/0310142 | |
| dc.identifier | Discrete Comput. Geom. 33 (2005), 669--686 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99250 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 52B11 (Primary); 52B12, 52B05 (Secondary) | |
| dc.title | Lower bounds for simplicial covers and triangulations of cubes | |
| dc.type | text |