Characterization of the OU matrix of a braid diagram
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916850934218752 |
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| author | Shimizu, Ayaka Yaguchi, Yoshiro |
| author_facet | Shimizu, Ayaka Yaguchi, Yoshiro |
| contents | The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram is characterized for up to 5 strands. As an application, the crossing matrix of a positive pure braid is also characterized for up to 5 strands. Moreover, a standard form of the OU matrix is given and characterized for general braids of up to 5 strands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of the OU matrix of a braid diagram Shimizu, Ayaka Yaguchi, Yoshiro Geometric Topology The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram is characterized for up to 5 strands. As an application, the crossing matrix of a positive pure braid is also characterized for up to 5 strands. Moreover, a standard form of the OU matrix is given and characterized for general braids of up to 5 strands. |
| title | Characterization of the OU matrix of a braid diagram |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2502.16035 |