- Title
- Lower bound theorems for general polytopes
- Creator
- Pineda-Villavicencio, Guillermo; Ugon, Julien; Yost, David
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/169270
- Identifier
- vital:13991
- Identifier
-
https://doi.org/10.1016/j.ejc.2018.12.003
- Identifier
- ISBN:0195-6698
- Abstract
- For a d-dimensional polytope with v vertices, d + 1 <= v <= 2d, we calculate precisely the minimum possible number of m-dimensional faces, when m = 1 or m >= 0.62d. This confirms a conjecture of Grunbaum, for these values of m. For v = 2d + 1, we solve the same problem when m = 1 or d - 2; the solution was already known for m = d - 1. In all these cases, we give a characterisation of the minimising polytopes. We also show that there are many gaps in the possible number of m-faces: for example, there is no polytope with 80 edges in dimension 10, and a polytope with 407 edges can have dimension at most 23.
- Publisher
- Elsevier
- Relation
- European Journal of Combinatorics Vol. 79, no. (2019), p. 27-45; http://purl.org/au-research/grants/arc/DP180100602
- Rights
- Copyright © 2018 Elsevier Ltd
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Polytopes; Manifold; Simplicial complexes
- Full Text
- Reviewed
- Hits: 1048
- Visitors: 1359
- Downloads: 339
Thumbnail | File | Description | Size | Format | |||
---|---|---|---|---|---|---|---|
View Details Download | SOURCE1 | Submitted version | 406 KB | Adobe Acrobat PDF | View Details Download |