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arXiv · 1402.2125

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices

Alan Haynes·Henna Koivusalo
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Abstract

For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient condition of Rauzy, of an infinite family of non-trivial bounded remainder sets for any totally irrational toral rotation in any dimension.

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Alan Haynes, Henna Koivusalo. 2014-02-10. Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices. https://arxiv.org/abs/1402.2125

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