Report
The layer number of grids
| العنوان: | The layer number of grids |
|---|---|
| المؤلفون: | Ambrus, Gergely, Hsu, Alexander, Peng, Bo, Jan, Shiyu |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, Mathematics - Combinatorics, 52C45, 68U05, 52A05 |
| الوصف: | The peeling process is defined as follows: starting with a finite point set $X \subset \mathbb{R}^d$, we repeatedly remove the set of vertices of the convex hull of the current set of points. The number of peeling steps needed to completely delete the set $X$ is called the layer number of $X$. In this paper, we study the layer number of the $d$-dimensional integer grid $[n]^d$. We prove that for every $d \geq 1$, the layer number of $[n]^d$ is at least $\Omega\left(n^\frac{2d}{d+1}\right)$. On the other hand, we show that for every $d\geq 3$, it takes at most $O(n^{d - 9/11})$ steps to fully remove $[n]^d$. Our approach is based on an enhancement of the method used by Har-Peled and Lidick\'{y} for solving the 2-dimensional case. Comment: 7 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2009.13130 |
| رقم الانضمام: | edsarx.2009.13130 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |