Academic Journal
Polytopes and $C^1$-convex bodies
| Title: | Polytopes and $C^1$-convex bodies |
|---|---|
| Authors: | Karim Adiprasito, José Alejandro Samper |
| Contributors: | Episciences Iam, Coordination, Louis J. Billera and Isabella Novik |
| Source: | Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AT,..., Iss Proceedings (2014) |
| Publisher Information: | Centre pour la Communication Scientifique Directe (CCSD), 2014. |
| Publication Year: | 2014 |
| Subject Terms: | Polytopes, Approximation theory, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Lower bound theorem, geometric combinatorics, 01 natural sciences, Geometric Combinatorics, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], f-vector theory, lower bound theorem, polytopes, QA1-939, convex bodies, 0101 mathematics, approximation theory, Mathematics, [math.math-co] mathematics [math]/combinatorics [math.co] |
| Description: | The face numbers of simplicial polytopes that approximate $C^1$-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 $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity. Nous étudions les nombres de faces de polytopes simpliciaux qui se rapprochent de $C^1$-corps convexes dans la métrique Hausdorff. Plusieurs résultats structurels sur le skeleta de ces polytopes sont recherchées et utilisées pour calculer un théorème limite inférieure de cette classe de polytopes. Cela résout partiellement une conjecture formulée par Kalai en 1994: si une suite $\{P_n\}_{n=0}^{\infty}$ de polytopes simpliciaux converge vers une $C^1$-corps convexe dans la distance Hausdorff, puis les entrées du $g$-vecteur de $P_n$ convergent vers l’infini. |
| Document Type: | Article Conference object |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1365-8050 |
| DOI: | 10.46298/dmtcs.2399 |
| Access URL: | https://dmtcs.episciences.org/2399/pdf https://inria.hal.science/hal-01207607v1 https://inria.hal.science/hal-01207607v1/document https://doi.org/10.46298/dmtcs.2399 https://doaj.org/article/39899ff9e0e94726834977d1e0bde93c https://hal.inria.fr/hal-01207607/document https://dmtcs.episciences.org/2399/pdf https://dmtcs.episciences.org/2399 https://hal.inria.fr/hal-01207607 https://hal.archives-ouvertes.fr/hal-01207607v1 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....978bb7544757a3fc3fc93c9c1a535fa5 |
| Database: | OpenAIRE |
| ISSN: | 13658050 |
|---|---|
| DOI: | 10.46298/dmtcs.2399 |