论文标题
三个差距定理的对称性
Symmetries of the Three Gap Theorem
论文作者
论文摘要
三个差距定理指出，对于任何$α\ in \ mathbb {r} $和$ n \ in \ mathbb {n} $中的$ n \，$ \ {0α，1α，\ dots，（n -1）α\}的分数零件将单位循环分为单位循环，分别在大多数三个不同的长度上分配给单位圆圈。我们证明了对对称性的结果，该差距大小出现在圆上的顺序。
The Three Gap Theorem states that for any $α\in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0α, 1α, \dots, (N - 1)α\}$ partition the unit circle into gaps of at most three distinct lengths. We prove a result about symmetries in the order with which the sizes of gaps appear on the circle.
