Knots at Dartmouth

This site contains a collection of data that knot theorists may find useful in their experiments. This includes tables of DT codes for all prime knots with crossing number bounded by 19 and several knot polynomials.

Knot Data

The data sets are compressed using xz to save space. For large files over 30MB the maximum level of compression is used. This results in a 6:1 compression ratio, but also means it takes some time to decompress. To do this, you’ll need a tool that can handle xz files.

For most GNU, Linux, and FreeBSD users, this is built-in. If you are using GNOME as your desktop environment you can right-click the file and hit extract.

macOS users can use the built-in Archive Utility.

Windows users will need to download a recent version of 7-zip.

Data Sets

Jones Polynomial
HOMFLY-PT Polynomial
Khovanov Polynomial

Tools

The data was created using a combination of several libraries. If you wish to reproduce this data, you’ll need these installed.

  1. regina
    A powerful C++ library with routines for computing several knot invariants, including the Jones and Homfly polynomials.
  2. sage
    The knot library in sage contains many useful tools for converting between different representations of knots, and for the computation of certain knot polynomials.
  3. SnapPy
    A Python wrapper, and extension, of the C SnapPea library. This contains a valuable set of routines for working with knots.
  4. JavaKh
    A Java library used for computing the Khovanov polynomial. The original version does not compile on modern versions of OpenJDK. Nikolay Pultsin made some cosmetic changes that allow it to run. These can be found at https://github.com/geometer/JavaKh-v2/
  5. knot_data
    Our own set of tools and scripts.
  6. libtmpl
    An experimental library with new routines for the computation of knot invarients. Written in C.