![](data:image/png;base64,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)
12n
0064
(K12n
0064
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 11 4 8 6 11
Solving Sequence
4,9
5
6,10,11
12 3 2 1 8 7
c
4
c
9
c
11
c
3
c
2
c
1
c
8
c
7
c
5
, c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.37718 × 10
22
u
20
− 1.64184 × 10
23
u
19
+ ··· + 1.18107 × 10
25
d + 1.07557 × 10
24
,
− 6.27749 × 10
23
u
20
+ 1.76680 × 10
24
u
19
+ ··· + 2.36214 × 10
25
c − 1.96176 × 10
25
,
4.23740 × 10
23
u
20
− 1.22487 × 10
24
u
19
+ ··· + 1.18107 × 10
25
b + 1.27339 × 10
25
,
1.40999 × 10
24
u
20
− 3.56156 × 10
24
u
19
+ ··· + 1.18107 × 10
25
a + 8.01422 × 10
25
, u
21
− 3u
20
+ ··· − 32u + 32i
I
u
2
= h182575u
12
c − 236482u
12
+ ··· − 1091678c − 1127628,
152367u
12
c − 563814u
12
+ ··· − 1320834c + 1767620,
− 72875u
12
+ 44515u
11
+ ··· + 2792824b − 1858402,
− 112621u
12
− 236501u
11
+ ··· + 1396412a − 268784,
u
13
+ u
12
+ 8u
11
+ 7u
10
+ 22u
9
+ 18u
8
+ 20u
7
+ 21u
6
− u
5
+ 5u
4
+ 8u
3
− 9u
2
+ 4u − 4i
I
v
1
= ha, d, c − v, b − v − 1, v
2
+ v + 1i
I
v
2
= ha, d + v + 1, c + a, b − v − 1, v
2
+ v + 1i
I
v
3
= hc, d + 1, b, a − 1, v + 1i
I
v
4
= ha, da − cb + 1, dv − 1, cv + ba + bv −a −v, b
2
− b + 1i
* 5 irreducible components of dim
C
= 0, with total 52 representations.
* 1 irreducible components of dim
C
= 1
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