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| Main Authors: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2302.09607 |
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| _version_ | 1866909057500053504 |
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| author | Loquias, Manuel Joseph C. Santos, Rovin B. |
| author_facet | Loquias, Manuel Joseph C. Santos, Rovin B. |
| contents | A coloring of a planar semiregular tiling $\mathcal{T}$ is an assignment of a unique color to each tile of $\mathcal{T}$. If $G$ is the symmetry group of $\mathcal{T}$, we say that the coloring is perfect if every element of $G$ induces a permutation on the finite set of colors. If $\mathcal{T}$ is $k$-valent, then a coloring of $\mathcal{T}$ with $k$ colors is said to be precise if no two tiles of $\mathcal{T}$ sharing the same vertex have the same color. In this work, we obtain perfect precise colorings of some families of $k$-valent semiregular tilings in the plane, where $k\leq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09607 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perfect precise colorings of plane semiregular tilings Loquias, Manuel Joseph C. Santos, Rovin B. Combinatorics 05B45 (Primary), 52C20 (Secondary) A coloring of a planar semiregular tiling $\mathcal{T}$ is an assignment of a unique color to each tile of $\mathcal{T}$. If $G$ is the symmetry group of $\mathcal{T}$, we say that the coloring is perfect if every element of $G$ induces a permutation on the finite set of colors. If $\mathcal{T}$ is $k$-valent, then a coloring of $\mathcal{T}$ with $k$ colors is said to be precise if no two tiles of $\mathcal{T}$ sharing the same vertex have the same color. In this work, we obtain perfect precise colorings of some families of $k$-valent semiregular tilings in the plane, where $k\leq 6$. |
| title | Perfect precise colorings of plane semiregular tilings |
| topic | Combinatorics 05B45 (Primary), 52C20 (Secondary) |
| url | https://arxiv.org/abs/2302.09607 |