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Fast repetitivity in non-rectifiable Delone sets
Ashwin Bhat, Michael Dymond
https://arxiv.org/abs/2506.19114 https://arxiv.org/pdf/2…

Fast repetitivity in non-rectifiable Delone sets
We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\mathbb{R}^d$ with $d \geq 2$. We further obtain a close to optimal repetitivity function for such sets. The proof is based on the process of encoding a non-realisable density in a Delone set, due to Burago and Kleiner.