B-type coefficient polynomial

Noboru Ito; Mayuko Kon

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arXiv · 2603.25402

B-type coefficient polynomial

Noboru Ito·Mayuko Kon

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Abstract

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.

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BibTeX RIS

Noboru Ito, Mayuko Kon. 2026-03-26. B-type coefficient polynomial. https://arxiv.org/abs/2603.25402

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