|
| | | | |
| | | |
| Stat |
Members: 3644
Articles: 2'499'343
Articles rated: 2609
16 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
General Position Subsets and Independent Hyperplanes in d-Space | | Jean Cardinal
; Csaba D. Tóth
; David R. Wood
; | | Date: |
14 Oct 2014 | | Abstract: | ErdH{o}s asked what is the maximum number $alpha(n)$ such that every set of
$n$ points in the plane with no four on a line contains $alpha(n)$ points in
general position. We consider variants of this question for $d$-dimensional
point sets and generalize previously known bounds. In particular, we prove the
following two results for fixed $d$:
- Every set $H$ of $n$ hyperplanes in $mathbb{R}^d$ contains a subset
$Ssubseteq H$ of size at least $c left(n log n
ight)^{1/d}$, for some
constant $c=c(d)>0$, such that no cell of the arrangement of $H$ is bounded by
hyperplanes of $S$ only.
- Every set of $cq^dlog q$ points in $mathbb{R}^d$, for some constant
$c=c(d)>0$, contains a subset of $q$ cohyperplanar points or $q$ points in
general position.
Two-dimensional versions of the above results were respectively proved by
Ackerman et al. [Electronic J. Combinatorics, 2014] and by Payne and Wood [SIAM
J. Discrete Math., 2013]. | | Source: | arXiv, 1410.3637 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER