Weak rectangular diagrams, multi-crossing number, and arc index
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908824073404416 |
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| author | Ito, Tetsuya |
| author_facet | Ito, Tetsuya |
| contents | For a non-split multi-crossing diagram $D$ of a link $L$ we show that $α(L)-2 \leq c_2(D) + \sum_{n> 2}(2n-4)c_n(D)$ holds. Here $α(L)$ is the arc index and $c_n(D)$ is the number of $n$-crossings of $D$. This generalizes and subsumes many known inequalities related to multi-crossing numbers. In the course of proof, we introduce a notion of weak rectangular diagram and show that a loose rectangular diagram can be converted to usual rectangular diagram preserving its arc index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak rectangular diagrams, multi-crossing number, and arc index Ito, Tetsuya Geometric Topology For a non-split multi-crossing diagram $D$ of a link $L$ we show that $α(L)-2 \leq c_2(D) + \sum_{n> 2}(2n-4)c_n(D)$ holds. Here $α(L)$ is the arc index and $c_n(D)$ is the number of $n$-crossings of $D$. This generalizes and subsumes many known inequalities related to multi-crossing numbers. In the course of proof, we introduce a notion of weak rectangular diagram and show that a loose rectangular diagram can be converted to usual rectangular diagram preserving its arc index. |
| title | Weak rectangular diagrams, multi-crossing number, and arc index |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2507.01404 |