The LinKnot function
RationalKL (webMathematica RationalKL)
calculates the number and Conway symbols of all rational KLs
for a given number of crossings n. The results are given in the following
table:
|
| n = 2 |
|
| Links |
| 2 |
| No. of links:
1 |
|
| n = 3 |
|
| Knots |
| 3 |
| No. of knots:
1 |
|
| n = 4 |
|
| Knots |
| 2 2 |
| No. of knots:
1 |
|
| Links |
| 4 |
| No. of links:
1 |
|
| n
= 5 |
|
| Knots |
| 5 |
3 2 |
| No.
of knots: 2 |
|
| Links |
| 2
1 2 |
| No.
of links: 1 |
|
| n
= 6 |
|
| Knots |
| 4 2 |
3 1 2 |
2 1 1 2 |
| No.
of knots: 3 |
|
| Links |
| 6 |
3 3 |
2 2 2 |
| No.
of links: 3 |
|
| n
= 7 |
|
| Knots |
| 7 |
5 2 |
4 3 |
3 2 2 |
3 1 3 |
2 2 1 2 |
2 1 1 1 2 |
| No.
of knots: 7 |
|
| Links |
| 4 1 2 |
3 1 1 2 |
2 3 2 |
|
|
|
|
| No.
of links: 3 |
|
| n
= 8 |
|
| Knots |
| 6 2 |
5 1 2 |
4 4 |
4 1 3 |
4 1 1 2 |
3 3 2 |
| 3 2 1 2 |
3 1 1 3 |
3 1 1 1 2 |
2 3 1 2 |
2 2 2 2 |
2 2 1 1 2 |
| No.
of knots: 12 |
|
| Links |
| 8 |
5 3 |
4 2 2 |
3 2 3 |
3 1 2 2 |
2 4 2 |
| 2 1 2 1 2 |
2 1 1 1 1 2 |
|
|
|
|
| No.
of links: 8 |
|
| n
= 9 |
|
| Knots |
| 9 |
7 2 |
6 3 |
5 4 |
5 2 2 |
5 1 3 |
| 4 2 3 |
4 2 1 2 |
4 1 2 2 |
4 1 1 1 2 |
3 4 2 |
3 3 3 |
| 3 2 2 2 |
3 2 1 3 |
3 1 2 1 2 |
3 1 1 2 2 |
3 1 1 1 1 2 |
2 4 1 2 |
| 2 3 2 2 |
2 3 1 1 2 |
2 2 1 2 2 |
2 1 3 1 2 |
2 1 2 1 1 2 |
2 1 1 1 1 1 2 |
| No.
of knots: 24 |
|
| Links |
| 6 1 2 |
5 1 1 2 |
4 3 2 |
4 1 4 |
4 1 1 3 |
3 3 1 2 |
| 3 2 1 1 2 |
3 1 3 2 |
3 1 1 1 3 |
2 5 2 |
2 2 2 1 2 |
2 2 1 1 1 2 |
| No.
of links: 12 |
|
| n
= 10 |
|
| Knots |
| 8 2 |
7 1 2 |
6 4 |
6 1 3 |
6 1 1 2 |
| 5 3 2 |
5 2 1 2 |
5 1 4 |
5 1 1 3 |
5 1 1 1 2 |
| 4 3 3 |
4 3 1 2 |
4 2 2 2 |
4 2 1 1 2 |
4 1 3 2 |
| 4 1 2 3 |
4 1 1 4 |
4 1 1 2 2 |
4 1 1 1 3 |
3 5 2 |
| 3 4 1 2 |
3 3 1 3 |
3 3 1 1 2 |
3 2 3 2 |
3 2 2 1 2 |
| 3 2 1 1 3 |
3 2 1 1 1 2 |
3 1 3 1 2 |
3 1 2 2 2 |
3 1 2 1 1 2 |
| 3 1 1 3 2 |
3 1 1 1 2 2 |
3 1 1 1 1 3 |
2 5 1 2 |
2 4 2 2 |
| 2 4 1 1 2 |
2 3 3 2 |
2 3 1 2 2 |
2 2 3 1 2 |
2 2 2 1 1 2 |
| 2 2 1 2 1 2 |
2 2 1 1 1 1 2 |
2 1 2 2 1 2 |
2 1 2 1 1 1 2 |
2 1 1 1 1 1 1 2 |
| No.
of knots: 45 |
|
| Links |
| 7 3 |
6 2 2 |
5 5 |
5 2 3 |
5 1 2 2 |
| 4 4 2 |
4 2 4 |
4 2 1 3 |
4 1 2 1 2 |
4 1 1 1 1 2 |
| 3 4 3 |
3 3 2 2 |
3 2 2 3 |
3 2 1 2 2 |
3 1 4 2 |
| 3 1 2 1 3 |
3 1 1 2 1 2 |
3 1 1 1 1 1 2 |
2 6 2 |
2 3 2 1 2 |
| 2 3 1 1 1 2 |
2 2 2 2 2 |
2 2 1 1 2 2 |
2 1 4 1 2 |
2 1 3 1 1 2 |
| 2 1 1 2 1 1 2 |
10 |
|
|
|
| No.
of links: 27 |
  
|