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arXiv · 2208.01680

Symmetries of the Three Gap Theorem

Aneesh Dasgupta·Roland Roeder
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Abstract

The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ 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.

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Aneesh Dasgupta, Roland Roeder. 2022-08-02. Symmetries of the Three Gap Theorem. https://doi.org/10.1080/00029890.2022.2158021

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