$SL_2$-tilings with translational symmetry
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Bazier-Matte, Veronique Bourgie, Marie-Anne Felikson, Anna Tumarkin, Pavel |
| author_facet | Bazier-Matte, Veronique Bourgie, Marie-Anne Felikson, Anna Tumarkin, Pavel |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $SL_2$-tilings with translational symmetry Bazier-Matte, Veronique Bourgie, Marie-Anne Felikson, Anna Tumarkin, Pavel Combinatorics Rings and Algebras 13F60, 05E16 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. |
| title | $SL_2$-tilings with translational symmetry |
| topic | Combinatorics Rings and Algebras 13F60, 05E16 |
| url | https://arxiv.org/abs/2512.18810 |