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