B-type coefficient polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910075660009472 |
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| author | Ito, Noboru Kon, Mayuko |
| author_facet | Ito, Noboru Kon, Mayuko |
| contents | An A-type coefficient polynomial introduced by Kawauchi recovers the HOMFLY-PT polynomial as a formal power series within skein theory. A notable feature of this construction is that each coefficient defines a link invariant, yielding an infinite sequence of invariants, while the low-degree coefficients are relatively easy to compute. In this paper, we extend this viewpoint to the B-type setting. Unlike the A-type case, the B-type setting requires a genuinely new inductive scheme due to the four-term skein relation. More precisely, we introduce coefficient polynomials associated with the B-type skein relation and show that their generating series recovers the Kauffman polynomial. We further prove that these coefficient polynomials are well-defined and that the resulting generating series is invariant under the corresponding Reidemeister moves. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | B-type coefficient polynomial Ito, Noboru Kon, Mayuko Geometric Topology Combinatorics An A-type coefficient polynomial introduced by Kawauchi recovers the HOMFLY-PT polynomial as a formal power series within skein theory. A notable feature of this construction is that each coefficient defines a link invariant, yielding an infinite sequence of invariants, while the low-degree coefficients are relatively easy to compute. In this paper, we extend this viewpoint to the B-type setting. Unlike the A-type case, the B-type setting requires a genuinely new inductive scheme due to the four-term skein relation. More precisely, we introduce coefficient polynomials associated with the B-type skein relation and show that their generating series recovers the Kauffman polynomial. We further prove that these coefficient polynomials are well-defined and that the resulting generating series is invariant under the corresponding Reidemeister moves. |
| title | B-type coefficient polynomial |
| topic | Geometric Topology Combinatorics |
| url | https://arxiv.org/abs/2603.25402 |