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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/2502.14392 |
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| _version_ | 1866916622665515008 |
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| author | Esson, Jack Kastis, Eleftherios Schulze, Bernd |
| author_facet | Esson, Jack Kastis, Eleftherios Schulze, Bernd |
| contents | This paper provides a combinatorial characterisation for generic forced symmetric rigidity of bar-joint frameworks in the Euclidean plane that are symmetric with respect to the orientation-reversing wallpaper group $\mathbb{Z}^2\rtimes\mathcal{C}_s$, also known as $pm$ in crystallography, under a fixed lattice representation. Corresponding results for the wallpaper groups $cm$ and $pg$ follow directly from this. The method used also provides an inductive construction for the corresponding gain graphs, in terms of Henneberg-type graph operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orientation-Reversing Crystallographic Rigidity Esson, Jack Kastis, Eleftherios Schulze, Bernd Combinatorics 52C25, 05C22 This paper provides a combinatorial characterisation for generic forced symmetric rigidity of bar-joint frameworks in the Euclidean plane that are symmetric with respect to the orientation-reversing wallpaper group $\mathbb{Z}^2\rtimes\mathcal{C}_s$, also known as $pm$ in crystallography, under a fixed lattice representation. Corresponding results for the wallpaper groups $cm$ and $pg$ follow directly from this. The method used also provides an inductive construction for the corresponding gain graphs, in terms of Henneberg-type graph operations. |
| title | Orientation-Reversing Crystallographic Rigidity |
| topic | Combinatorics 52C25, 05C22 |
| url | https://arxiv.org/abs/2502.14392 |