### Abstract

We show that a Brunnian link of n components and the n component trivial link share the same first n -1 coefficients of the Jones-Conway (Homflypt) polynomial (answering the question of Kanenobu and Miyazawa). We prove also the similar result for the Kauffman polynomial of Brunnian links. We place our solution in the context of Vassiliev-Gusarov skein modules based on mixed singular crossings.

Original language | English |
---|---|

Pages (from-to) | 2799-2802 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 9 |

Publication status | Published - 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*129*(9), 2799-2802.

**The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings.** / Przytycki, Jözef H.; Taniyama, Kouki.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 129, no. 9, pp. 2799-2802.

}

TY - JOUR

T1 - The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings

AU - Przytycki, Jözef H.

AU - Taniyama, Kouki

PY - 2001

Y1 - 2001

N2 - We show that a Brunnian link of n components and the n component trivial link share the same first n -1 coefficients of the Jones-Conway (Homflypt) polynomial (answering the question of Kanenobu and Miyazawa). We prove also the similar result for the Kauffman polynomial of Brunnian links. We place our solution in the context of Vassiliev-Gusarov skein modules based on mixed singular crossings.

AB - We show that a Brunnian link of n components and the n component trivial link share the same first n -1 coefficients of the Jones-Conway (Homflypt) polynomial (answering the question of Kanenobu and Miyazawa). We prove also the similar result for the Kauffman polynomial of Brunnian links. We place our solution in the context of Vassiliev-Gusarov skein modules based on mixed singular crossings.

UR - http://www.scopus.com/inward/record.url?scp=33646849080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646849080&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646849080

VL - 129

SP - 2799

EP - 2802

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -