Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929511230078976 |
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| author | Kari, Jarkko Lutfalla, Victor |
| author_facet | Kari, Jarkko Lutfalla, Victor |
| contents | We present Planar Rosa, a family of rhombus tilings with a $2n$-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even $n\geq 4$. This completes our previously published results for odd values of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_08856 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry Kari, Jarkko Lutfalla, Victor Discrete Mathematics Combinatorics We present Planar Rosa, a family of rhombus tilings with a $2n$-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even $n\geq 4$. This completes our previously published results for odd values of $n$. |
| title | Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2203.08856 |