Cyclic Groups and the Three Distance Theorem
Cyclic Groups and the Three Distance Theorem
复制标题
循环群和三距离定理
DOI：
10.4153/cjm-2007-022-3
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
N. Chevallier
中科院分区：
文献类型：
--
作者：
N. Chevallier
Abstract We give a two dimensional extension of the three distance theorem. Let $\theta $ be in ${{\mathbf{R}}^{2}}$ and let $q$ be in $\mathbf{N}$ . There exists a triangulation of ${{\mathbf{R}}^{2}}$ invariant by ${{\mathbf{Z}}^{2}}$ -translations, whose set of vertices is ${{\mathbf{Z}}^{2}}\,+\,\{0,\,\theta ,\,\ldots ,\,q\theta \}$ , and whose number of different triangles, up to translations, is bounded above by a constant which does not depend on $\theta $ and $q$ .
Abstract We give a two dimensional extension of the three distance theorem. Let $\theta $ be in ${{\mathbf{R}}^{2}}$ and let $q$ be in $\mathbf{N}$ . There exists a triangulation of ${{\mathbf{R}}^{2}}$ invariant by ${{\mathbf{Z}}^{2}}$ -translations, whose set of vertices is ${{\mathbf{Z}}^{2}}\,+\,\{0,\,\theta ,\,\ldots ,\,q\theta \}$ , and whose number of different triangles, up to translations, is bounded above by a constant which does not depend on $\theta $ and $q$ .