Twist polynomial as a weight system for set systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929315353985024 |
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| author | Deng, Qingying Jin, Xian'an Yan, Qi |
| author_facet | Deng, Qingying Jin, Xian'an Yan, Qi |
| contents | Recently, Chmutov proved that the partial-dual polynomial considered as a function on chord diagrams satisfies the four-term relation. Deng et al. then proved that this function on framed chord diagrams also satisfies the four-term relation, i.e., is a framed weight system. In this paper, we extend their results to the twist polynomial of a set system by proving that the twist polynomial on set systems satisfies the four-term relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twist polynomial as a weight system for set systems Deng, Qingying Jin, Xian'an Yan, Qi Combinatorics 05C10 05C65 57M15 57Q15 Recently, Chmutov proved that the partial-dual polynomial considered as a function on chord diagrams satisfies the four-term relation. Deng et al. then proved that this function on framed chord diagrams also satisfies the four-term relation, i.e., is a framed weight system. In this paper, we extend their results to the twist polynomial of a set system by proving that the twist polynomial on set systems satisfies the four-term relation. |
| title | Twist polynomial as a weight system for set systems |
| topic | Combinatorics 05C10 05C65 57M15 57Q15 |
| url | https://arxiv.org/abs/2404.10216 |