On the Constant of Homothety for Covering a Convex Set with Its Smaller Copies
| dc.creator | Naszodi, Marton | |
| dc.date | 2009-01-17 | |
| dc.date.accessioned | 2026-07-07T12:31:29Z | |
| dc.date.available | 2026-07-07T12:31:29Z | |
| dc.description | Let $H_d$ denote the smallest integer $n$ such that for every convex body $K$ in $\Re^d$ there is a $0<λ< 1$ such that $K$ is covered by $n$ translates of $λK$. In the book \emph{Research problems in discrete geometry.} by Brass, Moser and Pach, the following problem was posed: Is there a $0<λ_d<1$ depending on $d$ only with the property that every convex body $K$ in $\Re^d$ is covered by $H_d$ translates of $λ_d K$? We prove the affirmative answer to the question and hence show that the Gohberg--Markus--Boltyanski--Hadwiger Conjecture (according to which $H_d\leq 2^d$) holds if, and only if, a formally stronger version of it holds. | |
| dc.description | 4 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0901.2652 | |
| dc.identifier | http://arxiv.org/abs/0901.2652 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216461 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 52A35, 52A20, 52C17 | |
| dc.title | On the Constant of Homothety for Covering a Convex Set with Its Smaller Copies | |
| dc.type | text |