Name
Abstract | ||
|---|---|---|
We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n >= 7 can be obtained as a section of a (2 + [n/7])-dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014). |
Year | Venue | Keywords |
|---|---|---|
2015 | ELECTRONIC JOURNAL OF COMBINATORICS | polygon,polytope projections and sections,extension complexity,non-negative rank,nonrealizability,pseudo-line arrangements |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Polygon,Vertex (geometry),Matrix (mathematics),Nonnegative rank,Heptagon,Polytope,Mathematics | Journal | 22.0 |
Issue | ISSN | Citations |
1.0 | 1077-8926 | 4 |
PageRank | References | Authors |
0.52 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arnau Padrol | 1 | 32 | 7.93 |
| Julian Pfeifle | 2 | 31 | 6.56 |