12n
0273
(K12n
0273
)
A knot diagram
1
Linearized knot diagam
3 4 11 2 10 4 12 3 6 9 7 8
Solving Sequence
7,11
12 8
1,4
3 9 2 5 6 10
c
11
c
7
c
12
c
3
c
8
c
2
c
4
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
7
− 12u
6
+ 30u
5
+ 104u
4
+ 50u
3
− 36u
2
+ 4b + 4u + 12,
6u
7
+ 15u
6
− 36u
5
− 130u
4
− 62u
3
+ 54u
2
+ 4a − 4u − 20,
u
8
+ 4u
7
− 2u
6
− 30u
5
− 44u
4
− 12u
3
+ 8u
2
− 4u − 4i
I
u
2
= h−au + b + 2a − u + 2, 2a
2
− au + 2a + u + 3, u
2
− 2i
I
u
3
= hu
2
+ 2b + 2a − 4u + 2, 4u
2
a + 2a
2
− 12au − u
2
+ 6a + 7u − 6, u
3
− 4u
2
+ 4u − 2i
I
u
4
= h2b + 2a + u + 2, 2a
2
+ 2au + 2a + u + 3, u
2
− 2i
I
v
1
= ha, b
2
− b + 1, v + 1i
I
v
2
= ha, b + v −1, v
2
− v + 1i
* 6 irreducible components of dim
C
= 0, with total 26 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1