Knot family: p
(p = 2k+1)
Notation:
3
31
5
51
7
71
9
91
Dowker codes:
3
4 6 2
5
6 8 10 2 4
7
8 10 12 14 2 4 6
9
10 12 14 16 18 2 4 6 8
11
12 14 16 18 20 22 2 4 6 8 10
13
14 16 18 20 22 24 26 2 4 6 8 10 12
15
16 18 20 22 24 26 28 30 2 4 6 8 10
12 14
17
18 20 22 24 26 28 30 32 34 2 4 6 8
10 12 14 16
19
20 22 24 26 28 30 32 34 36 38 2 4 6 8
10 12 14 16 18
Alexander polynomials:
3
[1 -1
5
[1 -1 1
7
[1 -1 1 -1
9
[1 -1 1 -1 1
11
[1 -1 1 -1 1 -1
13
[1 -1 1 -1 1 -1 1
15
[1 -1 1 -1 1 -1 1 -1
17
[1 -1 1 -1 1 -1 1 -1 1
19
[1 -1 1 -1 1 -1 1 -1 1 -1
D( p ) = |
2k
å
i = 0 |
(-1) i t i |
|
Jones polynomials:
3
1 4 1 0 1 -1
5
2 7 1 0 1 -1 1 -1
7
3 10 1 0 1 -1 1 -1 1 -1
9
4 13 1 0 1 -1 1 -1 1 -1 1 -1
11
5 16 1 0 1 -1 1 -1 1 -1 1 -1 1 -1
13
6 19 1 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
15
7 22 1 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
17
8 25 1 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
19
9 28 1 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
1 -1
Symmetry groups: D1
Symmetry type: chiral, reversible.
Signatures: 2k
Unknotting numbers: k
|