Jones rational coincidences

Ruth Lawrence*, Ori Rosenstein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We investigate coincidences of the (one-variable) Jones polynomial amongst rational knots, what we call "Jones rational coincidences". We provide moves on the continued fraction expansion of the associated rational which we prove do not change the Jones polynomial and conjecture (based on experimental evidence from all rational knots with determinant <900) that these moves are sufficient to generate all Jones rational coincidences. In the process we give a new formula for the Jones polynomial of a rational knot based on a continued fraction expansion of the associated rational, which has significantly fewer terms than other formulae known to us. The paper is based on the second author's Ph.D. thesis and gives an essentially self-contained account.

Original languageAmerican English
Article number2340015
JournalJournal of Knot Theory and its Ramifications
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.


  • Jones polynomial
  • rational knots
  • rational tangles


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