K14a6801
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
4 12 14 18 22 26 2 8 20 6 16 28 10 24
Notes on presentations of K14a6801
Polynomial invariants
Jones polynomial
Data:K14a6801/Jones Polynomial
Alexander polynomial
2
t
4
−
16
t
3
+
49
t
2
−
83
t
+
97
−
83
t
−
1
+
49
t
−
2
−
16
t
−
3
+
2
t
−
4
{\displaystyle 2t^{4}-16t^{3}+49t^{2}-83t+97-83t^{-1}+49t^{-2}-16t^{-3}+2t^{-4}}
Conway polynomial
Data:K14a6801/Conway Polynomial
Determinant
Data:K14a6801/Determinant
Signature
Data:K14a6801/Signature
HOMFLY-PT polynomial
z
8
a
−
4
+
z
8
a
−
6
−
2
z
6
a
−
2
+
2
z
6
a
−
4
+
2
z
6
a
−
6
−
2
z
6
a
−
8
−
5
z
4
a
−
2
+
z
4
a
−
4
−
5
z
4
a
−
8
+
z
4
a
−
10
+
z
4
−
3
z
2
a
−
2
+
3
z
2
a
−
4
−
z
2
a
−
6
−
2
z
2
a
−
8
+
2
z
2
a
−
10
+
2
z
2
−
a
−
2
+
2
a
−
4
−
a
−
6
+
1
{\displaystyle z^{8}a^{-4}+z^{8}a^{-6}-2z^{6}a^{-2}+2z^{6}a^{-4}+2z^{6}a^{-6}-2z^{6}a^{-8}-5z^{4}a^{-2}+z^{4}a^{-4}-5z^{4}a^{-8}+z^{4}a^{-10}+z^{4}-3z^{2}a^{-2}+3z^{2}a^{-4}-z^{2}a^{-6}-2z^{2}a^{-8}+2z^{2}a^{-10}+2z^{2}-a^{-2}+2a^{-4}-a^{-6}+1}
Kauffman polynomial
z
13
$
F
a
i
l
e
d
−
1
+
z
13
$
F
a
i
l
e
d
−
1
+
4
z
12
$
F
a
i
l
e
d
−
1
+
8
z
12
$
F
a
i
l
e
d
−
1
+
4
z
12
$
F
a
i
l
e
d
−
1
+
7
z
11
$
F
a
i
l
e
d
−
1
+
15
z
11
$
F
a
i
l
e
d
−
1
+
16
z
11
$
F
a
i
l
e
d
−
1
+
8
z
11
$
F
a
i
l
e
d
−
1
+
7
z
10
$
F
a
i
l
e
d
−
1
+
7
z
10
$
F
a
i
l
e
d
−
1
+
4
z
10
$
F
a
i
l
e
d
−
1
+
15
z
10
$
F
a
i
l
e
d
−
1
+
11
z
10
$
F
a
i
l
e
d
−
1
+
4
z
9
$
F
a
i
l
e
d
−
1
−
11
z
9
$
F
a
i
l
e
d
−
1
−
32
z
9
$
F
a
i
l
e
d
−
1
−
23
z
9
$
F
a
i
l
e
d
−
1
+
5
z
9
$
F
a
i
l
e
d
−
1
+
11
z
9
$
F
a
i
l
e
d
−
1
−
21
z
8
$
F
a
i
l
e
d
−
1
−
42
z
8
$
F
a
i
l
e
d
−
1
−
42
z
8
$
F
a
i
l
e
d
−
1
−
39
z
8
$
F
a
i
l
e
d
−
1
−
9
z
8
$
F
a
i
l
e
d
−
1
+
8
z
8
$
F
a
i
l
e
d
−
1
+
z
8
−
15
z
7
$
F
a
i
l
e
d
−
1
−
17
z
7
$
F
a
i
l
e
d
−
1
−
6
z
7
$
F
a
i
l
e
d
−
1
−
17
z
7
$
F
a
i
l
e
d
−
1
−
33
z
7
$
F
a
i
l
e
d
−
1
−
16
z
7
$
F
a
i
l
e
d
−
1
+
4
z
7
$
F
a
i
l
e
d
−
1
+
14
z
6
$
F
a
i
l
e
d
−
1
+
30
z
6
$
F
a
i
l
e
d
−
1
+
27
z
6
$
F
a
i
l
e
d
−
1
+
23
z
6
$
F
a
i
l
e
d
−
1
−
7
z
6
$
F
a
i
l
e
d
−
1
−
14
z
6
$
F
a
i
l
e
d
−
1
+
z
6
$
F
a
i
l
e
d
−
1
−
4
z
6
+
19
z
5
$
F
a
i
l
e
d
−
1
+
33
z
5
$
F
a
i
l
e
d
−
1
+
33
z
5
$
F
a
i
l
e
d
−
1
+
40
z
5
$
F
a
i
l
e
d
−
1
+
36
z
5
$
F
a
i
l
e
d
−
1
+
7
z
5
$
F
a
i
l
e
d
−
1
−
8
z
5
$
F
a
i
l
e
d
−
1
+
6
z
4
$
F
a
i
l
e
d
−
1
+
7
z
4
$
F
a
i
l
e
d
−
1
+
8
z
4
$
F
a
i
l
e
d
−
1
+
2
z
4
$
F
a
i
l
e
d
−
1
+
11
z
4
$
F
a
i
l
e
d
−
1
+
8
z
4
$
F
a
i
l
e
d
−
1
−
2
z
4
$
F
a
i
l
e
d
−
1
+
6
z
4
−
9
z
3
$
F
a
i
l
e
d
−
1
−
14
z
3
$
F
a
i
l
e
d
−
1
−
17
z
3
$
F
a
i
l
e
d
−
1
−
22
z
3
$
F
a
i
l
e
d
−
1
−
15
z
3
$
F
a
i
l
e
d
−
1
+
5
z
3
$
F
a
i
l
e
d
−
1
−
7
z
2
$
F
a
i
l
e
d
−
1
−
10
z
2
$
F
a
i
l
e
d
−
1
−
9
z
2
$
F
a
i
l
e
d
−
1
−
2
z
2
$
F
a
i
l
e
d
−
1
−
3
z
2
$
F
a
i
l
e
d
−
1
−
2
z
2
$
F
a
i
l
e
d
−
1
+
z
2
$
F
a
i
l
e
d
−
1
−
4
z
2
+
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
+
4
z
$
F
a
i
l
e
d
−
1
+
3
z
$
F
a
i
l
e
d
−
1
−
z
$
F
a
i
l
e
d
−
1
−
z
$
F
a
i
l
e
d
−
1
+
$
F
a
i
l
e
d
−
1
+
2
$
F
a
i
l
e
d
−
1
+
$
F
a
i
l
e
d
−
1
+
1
{\displaystyle z^{13}\$Failed^{-1}+z^{13}\$Failed^{-1}+4z^{12}\$Failed^{-1}+8z^{12}\$Failed^{-1}+4z^{12}\$Failed^{-1}+7z^{11}\$Failed^{-1}+15z^{11}\$Failed^{-1}+16z^{11}\$Failed^{-1}+8z^{11}\$Failed^{-1}+7z^{10}\$Failed^{-1}+7z^{10}\$Failed^{-1}+4z^{10}\$Failed^{-1}+15z^{10}\$Failed^{-1}+11z^{10}\$Failed^{-1}+4z^{9}\$Failed^{-1}-11z^{9}\$Failed^{-1}-32z^{9}\$Failed^{-1}-23z^{9}\$Failed^{-1}+5z^{9}\$Failed^{-1}+11z^{9}\$Failed^{-1}-21z^{8}\$Failed^{-1}-42z^{8}\$Failed^{-1}-42z^{8}\$Failed^{-1}-39z^{8}\$Failed^{-1}-9z^{8}\$Failed^{-1}+8z^{8}\$Failed^{-1}+z^{8}-15z^{7}\$Failed^{-1}-17z^{7}\$Failed^{-1}-6z^{7}\$Failed^{-1}-17z^{7}\$Failed^{-1}-33z^{7}\$Failed^{-1}-16z^{7}\$Failed^{-1}+4z^{7}\$Failed^{-1}+14z^{6}\$Failed^{-1}+30z^{6}\$Failed^{-1}+27z^{6}\$Failed^{-1}+23z^{6}\$Failed^{-1}-7z^{6}\$Failed^{-1}-14z^{6}\$Failed^{-1}+z^{6}\$Failed^{-1}-4z^{6}+19z^{5}\$Failed^{-1}+33z^{5}\$Failed^{-1}+33z^{5}\$Failed^{-1}+40z^{5}\$Failed^{-1}+36z^{5}\$Failed^{-1}+7z^{5}\$Failed^{-1}-8z^{5}\$Failed^{-1}+6z^{4}\$Failed^{-1}+7z^{4}\$Failed^{-1}+8z^{4}\$Failed^{-1}+2z^{4}\$Failed^{-1}+11z^{4}\$Failed^{-1}+8z^{4}\$Failed^{-1}-2z^{4}\$Failed^{-1}+6z^{4}-9z^{3}\$Failed^{-1}-14z^{3}\$Failed^{-1}-17z^{3}\$Failed^{-1}-22z^{3}\$Failed^{-1}-15z^{3}\$Failed^{-1}+5z^{3}\$Failed^{-1}-7z^{2}\$Failed^{-1}-10z^{2}\$Failed^{-1}-9z^{2}\$Failed^{-1}-2z^{2}\$Failed^{-1}-3z^{2}\$Failed^{-1}-2z^{2}\$Failed^{-1}+z^{2}\$Failed^{-1}-4z^{2}+z\$Failed^{-1}+2z\$Failed^{-1}+2z\$Failed^{-1}+4z\$Failed^{-1}+3z\$Failed^{-1}-z\$Failed^{-1}-z\$Failed^{-1}+\$Failed^{-1}+2\$Failed^{-1}+\$Failed^{-1}+1}
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