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Zeros of the Jones polynomials for families of pretzel links

Author

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  • Jin, Xian'an
  • Zhang, Fuji

Abstract

In this paper, a general method for computing the Tutte polynomial of the subdivision of a graph is explained. As an application to the subdivision of sheaf graph which consists of two vertices joined by some parallel edges, we obtain the explicit expressions of the Jones polynomials for some families of the pretzel links. Motivated by the work of Chang and Shrock, we investigate the zeros distribution of its Jones polynomial for each family when the number of crossings goes to infinity, and generalize some of their results.

Suggested Citation

  • Jin, Xian'an & Zhang, Fuji, 2003. "Zeros of the Jones polynomials for families of pretzel links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 391-408.
    • Handle: RePEc:eee:phsmap:v:328:y:2003:i:3:p:391-408
    DOI: 10.1016/S0378-4371(03)00585-5
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    References listed on IDEAS

    as
    1. Chang, S.-C. & Shrock, R., 2001. "Zeros of Jones polynomials for families of knots and links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 196-218.
    2. Shrock, Robert, 2000. "Exact Potts model partition functions on ladder graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 388-446.
    3. Chang, Shu-Chiuan & Shrock, Robert, 2000. "Exact Potts model partition function on strips of the triangular lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(1), pages 189-238.
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    Cited by:

    1. Kassenova, T.K. & Tsyba, P.Yu. & Razina, O.V. & Myrzakulov, R., 2022. "Three-partite vertex model and knot invariants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    2. Jin, Xian'an & Zhang, Fuji, 2004. "Jones polynomials and their zeros for a family of links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 183-196.

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