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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18810 |
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Table of Contents:
- An $SL_2$-tiling is a bi-infinite matrix in which all adjacent $2 \times 2$ minors are equal to $1$. Positive integral $SL_2$-tilings were introduced by Assem, Reutenauer and Smith as generalisations of classical Conway--Coxeter frieze patterns. We show that positive integral $SL_2$-tilings with translational symmetry are in bijection with triangulations of annuli. We use this correspondence to study the properties of periodic positive integral $SL_2$-tilings.