三间隙定理的对称性
数论
2023-04-04 v1 组合数学
动力系统
摘要
三间隙定理指出，对于任意 和 ，集合 的小数部分将单位圆划分为至多三种不同长度的间隙。我们证明了关于这些间隙大小在圆上出现的顺序所具有的对称性的一项结果。
引用
@article{arxiv.2208.01680,
title = {Symmetries of the Three Gap Theorem},
author = {Aneesh Dasgupta and Roland Roeder},
journal= {arXiv preprint arXiv:2208.01680},
year = {2023}
}
备注
To appear in The American Math Monthly. This is the author's original manuscript (AOM), and this version does not include several improvements that took place due to the refereeing process. Comments welcome!