Wildest $\mathrm{SL}_2$-tilings

Andrei Zabolotskii

doi:10.1016/j.exco.2025.100206

Wildest $\mathrm{SL}_2$-tilings

Combinatorics 2025-11-10 v2

Authors: Andrei Zabolotskii

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Abstract

Tame SL $_2$ -tilings are related to Farey graph and friezes; much less is known about wild (not tame) SL $_2$ -tilings. In this note, we demonstrate SL $_2$ -tilings that are maximally wild: we prove that the maximum wild density of an integer SL $_2$ -tiling is $\tfrac25$ and present SL $_2$ -tilings over $\mathbb{Z}/N\mathbb{Z}$ with wild density 1.

Cite

@article{arxiv.2508.09773,
  title  = {Wildest $\mathrm{SL}_2$-tilings},
  author = {Andrei Zabolotskii},
  journal= {arXiv preprint arXiv:2508.09773},
  year   = {2025}
}

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7 pages

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