- Title
- Almost simplicial polytopes : the lower and upper bound theorems
- Creator
- Nevo, Eran; Pineda-Villavicencio, Guillermo; Ugon, Julien; Yost, David
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/172103
- Identifier
- vital:14449
- Identifier
-
https://doi.org/10.4153/S0008414X18000123
- Identifier
- ISBN:0008-414X (ISSN)
- Abstract
- We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of, and, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where s = 0. We characterize the minimizers and provide examples of maximizers for any. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest. © 2018 Canadian Mathematical Society.
- Publisher
- Cambridge University Press
- Relation
- Canadian Journal of Mathematics Vol. 72, no. 2 (2020), p. 537-556. http://purl.org/au-research/grants/arc/DP180100602
- Rights
- Copyright ©Canadian Mathematical Society 2018
- Rights
- This metadata is freely available under a CCO license
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Almost simplicial polytope; F-vector; Graph rigidity; H-vector; Lower Bound theorem; Polytope; Simplicial polytope; Upper Bound theorem
- Full Text
- Reviewed
- Hits: 3045
- Visitors: 3144
- Downloads: 219
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE2 | Accepted | 316 KB | Adobe Acrobat PDF | View Details Download |