Flag vectors of multiplicial polytopes
| dc.creator | Bayer, Margaret M. | |
| dc.date | 2003-12-04 | |
| dc.date.accessioned | 2026-07-07T05:03:34Z | |
| dc.date.available | 2026-07-07T05:03:34Z | |
| dc.description | Bisztriczky introduced the multiplex as a generalization of the simplex. A polytope is multiplicial if all its faces are multiplexes. In this paper it is proved that the flag vectors of multiplicial polytopes depend only on their face vectors. A special class of multiplicial polytopes, also discovered by Bisztriczky, is comprised of the ordinary polytopes. These are a natural generalization of the cyclic polytopes. The flag vectors of ordinary polytopes are determined. This is used to give a surprisingly simple formula for the h-vector of the ordinary d-polytope with n+1 vertices and characteristic k: h_i=binom{k-d+i}{i}+(n-k)binom{k-d+i-1}{i-1}, for i at most d/2. In addition, a construction is given for 4-dimensional multiplicial polytopes having two-thirds of their vertices on a single facet, answering a question of Bisztriczky. | |
| dc.description | 12 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0312112 | |
| dc.identifier | http://arxiv.org/abs/math/0312112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69474 | |
| dc.subject | Combinatorics | |
| dc.subject | 52B05 (Primary); 52B11, 52B12 (Secondary) | |
| dc.title | Flag vectors of multiplicial polytopes | |
| dc.type | text |