On the Connectedness of Rational Arithmetic Discrete Hyperplanes
On the Connectedness of Rational Arithmetic Discrete Hyperplanes
复制标题
论有理算术离散超平面的连通性
DOI：
10.1007/11907350_19
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
D. Jamet;Jean
虽然连通算术离散线完全由其算术厚度表征，但对于任意维的算术离散超平面，仅存在部分结果。在本文中，我们主要关注0-连通有理数算术离散平面的研究。通过对给定整数向量的算术约简，给出了一个计算具有法向量的最薄0-连通算术平面的厚度的算法。
While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in ℤ3. Thanks to an arithmetic reduction on a given integer vectorn, we provide an algorithm which computes the thickness of the thinnest 0-connected arithmetic plane with normal vectorn.