Abstract
The face numbers of simplicial polytopes that approximate C1-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence {Pn}8n=0 of simplicial polytopes converges to a C1-convex body in the Hausdorff distance, then the entries of the g-vector of Pn converge to infinity.
Original language | English (US) |
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Pages (from-to) | 277-287 |
Number of pages | 11 |
Journal | Discrete Mathematics and Theoretical Computer Science |
State | Published - 2014 |
Externally published | Yes |
Event | 26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States Duration: Jun 29 2014 → Jul 3 2014 |
Keywords
- Approximation theory
- Convex bodies
- F-vector theory
- Geometric Combinatorics
- Lower bound theorem
- Polytopes
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
- Discrete Mathematics and Combinatorics