Canonical projection tilings defined by patterns
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866910627628318720 |
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| author | Bédaride, Nicolas Fernique, Thomas |
| author_facet | Bédaride, Nicolas Fernique, Thomas |
| contents | We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local rules for canonical projection tilings, or subshift of finite type. This provides a link between algebraic properties of affine subspaces and combinatorics of their digitizations. The condition relies on the notion of {\em coincidence} and can be effectively checked. As a corollary, we get that only algebraic subspaces can be characterized by patterns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_06863 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Canonical projection tilings defined by patterns Bédaride, Nicolas Fernique, Thomas Dynamical Systems Discrete Mathematics Combinatorics Metric Geometry 52C23, 37B50 We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local rules for canonical projection tilings, or subshift of finite type. This provides a link between algebraic properties of affine subspaces and combinatorics of their digitizations. The condition relies on the notion of {\em coincidence} and can be effectively checked. As a corollary, we get that only algebraic subspaces can be characterized by patterns. |
| title | Canonical projection tilings defined by patterns |
| topic | Dynamical Systems Discrete Mathematics Combinatorics Metric Geometry 52C23, 37B50 |
| url | https://arxiv.org/abs/1812.06863 |