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I'm looking for a list of Gauss codes for knots 12 crossings and higher. I downloaded the list of all the knots up to 12 crossings from Charles Livingston's Knot Info. Are there any other online sources of Gauss codes?

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  • $\begingroup$ You may want to contact Morwen Thistlethwaite, who, I believe, has this data up to 16 crossings. $\endgroup$
    – Jim Conant
    Dec 6, 2016 at 5:20
  • $\begingroup$ I'm a little confused. It sounds like you already have the Gauss codes for prime knots with 12 or less crossings. Why are you looking for further resources? $\endgroup$ Dec 6, 2016 at 7:45
  • $\begingroup$ @JimConant I'll poke around a bit more to see if I can this information first before I contact him, but thanks! $\endgroup$
    – Daggrah
    Dec 6, 2016 at 17:22
  • $\begingroup$ @RyanBudney You're correct, I do have that information. An algorithm I wrote for my research involves Gauss codes, and it thus far has been successful for knots with 12 or fewer crossings. I'd like to check that this is the case for larger knots. $\endgroup$
    – Daggrah
    Dec 6, 2016 at 17:22

2 Answers 2

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Although this is not an online source like KnotInfo, Snappy has two censuses of 16 crossing knots: one for alternating knots and one for non-alternating knots. It doesn't immediately give you Gauss codes for these knots, but can give you DT code which carries the same information.

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You can generate your own Gauss codes: 1. Every Gauss code can be represented faithfully by a signed chord diagram, known as a Gauss diagram (Polyak and Viro 1994). 2. There is an efficient algorithm for generating essentially unique chord diagrams (J. Sawada 2002). 3. There is an criterion for determining the planarity of signed Gauss codes (J. Scott Carter 1991).

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