IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v328y2003i3p391-408.html
   My bibliography  Save this article

Zeros of the Jones polynomials for families of pretzel links

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103005855
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(03)00585-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chang, Shu-Chiuan & Shrock, Robert, 2023. "Measures of spin ordering in the Potts model with a generalized external magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    2. Wu, F.Y & Wang, J, 2001. "Zeroes of the Jones polynomial," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 483-494.
    3. Chang, Shu-Chiuan & Shrock, Robert, 2020. "Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. 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).
    5. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:328:y:2003:i:3:p:391-408. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.