By clicking at **this site** you may see
all distinct knots with up to **12** crossings. This table has been made
through a direct conversion of the computer output. We now explain the
meaning of the various symbols.

We start first with the list of knots.
For each knot, the first
line denotes its **referrence number**, starting from 0 for the
trivial knot, and ending to 2977 for the last 12 crossing knot. The second
line shows the actual notation of the knot, and is written in *italics*.
The meaning of the notation has been explained in a
**previous
page**. The following lines denote the HOMFLYPT polynomials as follows:
a term *c(m,n)* indicates the existence of a term *c* times
*x**m* times *y**n* in the HOMFLYPT polynomial.

Once all knots have thus been presented, we continue by showing how knots
with identical polynomials are distinguished. First, we list the groups of
knots sharing the same (or symmetrical) polynomials. We continue with the
colorization invariants. We only list the invariants and the groups of knots
where distinctness is shown through unequal number of coloring possibilities.
Each colorization is presented through a *partition* of some positive
integer, indicating that the colorization used corresponds to a conjugacy
class of the permutation group that corresponds to such a partition. Knots
here are presented through their referrence numbers, which were given before.

One may check that at the end of the file, all knots have been shown distinct to each other either through the HOMFLYPT polynomials, or through some colorization invariant.