This website contains computational results
on small connected quandles and their knot colorings
obtained by
W. Edwin Clark and
Timothy Yeatman.
Go to Quandle Cocycle Knot Invariants for backgound material on quandles and their knot colorings.
Applications of these computational results can be found at the website Quandle Colorings and Invariants of Knots in the Table.
The paper Quandle Colorings and of Knots and Applications is based on computations posted in this and the above mentioned websites.
The list of 12965 knots contains the sequence Knot[i], i = 1,...,12965, that are (representatives of) all prime oriented knots with at most 13 crossings. The first entry of the list Knot[i] is the name of the knot, the second is the braid index, the third is the length of the braid, the fourth is the braid description of the knot. These are from J. C. Cha and C. Livingston, http://www.indiana.edu/~knotinfo/, (up to 12 crossings) and the remaining 13 crossing knots from Alexander Stoimenow, http://stoimenov.net/stoimeno/homepage/ptab/index.html.
The quandles in the RIG package are left distributive. To conform with our convention that quandles are right distributive, we use the transpose of the quandle matrices in RIG and we call them RIG quandles. The quandle in RIG denoted by SmallQuandle(n,j) we denote by C[n,j]. We also denote the i-th quandle in lexicographical order on the pairs (n,j) by RIG[i]. A file containing these quandle can be found below.