K14n11818
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
4 10 18 12 2 20 -24 -26 -22 28 8 -16 -14 6
Notes on presentations of K14n11818
Polynomial invariants
Jones polynomial
Data:K14n11818/Jones Polynomial
Alexander polynomial
−
2
t
4
+
13
t
3
−
33
t
2
+
54
t
−
63
+
54
t
−
1
−
33
t
−
2
+
13
t
−
3
−
2
t
−
4
{\displaystyle -2t^{4}+13t^{3}-33t^{2}+54t-63+54t^{-1}-33t^{-2}+13t^{-3}-2t^{-4}}
Conway polynomial
Data:K14n11818/Conway Polynomial
Determinant
Data:K14n11818/Determinant
Signature
Data:K14n11818/Signature
HOMFLY-PT polynomial
−
z
8
a
−
6
−
z
8
a
−
8
+
z
6
a
−
4
−
3
z
6
a
−
6
−
2
z
6
a
−
8
+
z
6
a
−
10
+
3
z
4
a
−
4
−
z
4
a
−
6
+
3
z
4
a
−
8
+
2
z
2
a
−
4
+
3
z
2
a
−
6
+
7
z
2
a
−
8
−
6
z
2
a
−
10
+
z
2
a
−
12
+
2
a
−
6
+
2
a
−
8
−
4
a
−
10
+
a
−
12
{\displaystyle -z^{8}a^{-6}-z^{8}a^{-8}+z^{6}a^{-4}-3z^{6}a^{-6}-2z^{6}a^{-8}+z^{6}a^{-10}+3z^{4}a^{-4}-z^{4}a^{-6}+3z^{4}a^{-8}+2z^{2}a^{-4}+3z^{2}a^{-6}+7z^{2}a^{-8}-6z^{2}a^{-10}+z^{2}a^{-12}+2a^{-6}+2a^{-8}-4a^{-10}+a^{-12}}
Kauffman polynomial
2
z
12
$
F
a
i
l
e
d
−
1
+
2
z
12
$
F
a
i
l
e
d
−
1
+
6
z
11
$
F
a
i
l
e
d
−
1
+
13
z
11
$
F
a
i
l
e
d
−
1
+
7
z
11
$
F
a
i
l
e
d
−
1
+
7
z
10
$
F
a
i
l
e
d
−
1
+
13
z
10
$
F
a
i
l
e
d
−
1
+
17
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
−
12
z
9
$
F
a
i
l
e
d
−
1
−
26
z
9
$
F
a
i
l
e
d
−
1
+
10
z
9
$
F
a
i
l
e
d
−
1
+
z
8
$
F
a
i
l
e
d
−
1
−
26
z
8
$
F
a
i
l
e
d
−
1
−
61
z
8
$
F
a
i
l
e
d
−
1
−
55
z
8
$
F
a
i
l
e
d
−
1
−
16
z
8
$
F
a
i
l
e
d
−
1
+
5
z
8
$
F
a
i
l
e
d
−
1
−
16
z
7
$
F
a
i
l
e
d
−
1
−
10
z
7
$
F
a
i
l
e
d
−
1
−
3
z
7
$
F
a
i
l
e
d
−
1
−
22
z
7
$
F
a
i
l
e
d
−
1
−
12
z
7
$
F
a
i
l
e
d
−
1
+
z
7
$
F
a
i
l
e
d
−
1
−
4
z
6
$
F
a
i
l
e
d
−
1
+
31
z
6
$
F
a
i
l
e
d
−
1
+
70
z
6
$
F
a
i
l
e
d
−
1
+
44
z
6
$
F
a
i
l
e
d
−
1
+
13
z
6
$
F
a
i
l
e
d
−
1
+
4
z
6
$
F
a
i
l
e
d
−
1
+
20
z
5
$
F
a
i
l
e
d
−
1
+
25
z
5
$
F
a
i
l
e
d
−
1
+
10
z
5
$
F
a
i
l
e
d
−
1
+
9
z
5
$
F
a
i
l
e
d
−
1
+
13
z
5
$
F
a
i
l
e
d
−
1
+
9
z
5
$
F
a
i
l
e
d
−
1
+
5
z
4
$
F
a
i
l
e
d
−
1
−
17
z
4
$
F
a
i
l
e
d
−
1
−
30
z
4
$
F
a
i
l
e
d
−
1
−
12
z
4
$
F
a
i
l
e
d
−
1
−
13
z
4
$
F
a
i
l
e
d
−
1
−
6
z
4
$
F
a
i
l
e
d
−
1
+
3
z
4
$
F
a
i
l
e
d
−
1
−
8
z
3
$
F
a
i
l
e
d
−
1
−
9
z
3
$
F
a
i
l
e
d
−
1
+
11
z
3
$
F
a
i
l
e
d
−
1
+
10
z
3
$
F
a
i
l
e
d
−
1
−
10
z
3
$
F
a
i
l
e
d
−
1
−
8
z
3
$
F
a
i
l
e
d
−
1
−
2
z
2
$
F
a
i
l
e
d
−
1
+
7
z
2
$
F
a
i
l
e
d
−
1
+
2
z
2
$
F
a
i
l
e
d
−
1
−
5
z
2
$
F
a
i
l
e
d
−
1
+
4
z
2
$
F
a
i
l
e
d
−
1
+
z
2
$
F
a
i
l
e
d
−
1
−
z
2
$
F
a
i
l
e
d
−
1
−
7
z
$
F
a
i
l
e
d
−
1
−
6
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
+
z
$
F
a
i
l
e
d
−
1
−
2
$
F
a
i
l
e
d
−
1
+
2
$
F
a
i
l
e
d
−
1
+
4
$
F
a
i
l
e
d
−
1
+
$
F
a
i
l
e
d
−
1
{\displaystyle 2z^{12}\$Failed^{-1}+2z^{12}\$Failed^{-1}+6z^{11}\$Failed^{-1}+13z^{11}\$Failed^{-1}+7z^{11}\$Failed^{-1}+7z^{10}\$Failed^{-1}+13z^{10}\$Failed^{-1}+17z^{10}\$Failed^{-1}+11z^{10}\$Failed^{-1}+4z^{9}\$Failed^{-1}-12z^{9}\$Failed^{-1}-26z^{9}\$Failed^{-1}+10z^{9}\$Failed^{-1}+z^{8}\$Failed^{-1}-26z^{8}\$Failed^{-1}-61z^{8}\$Failed^{-1}-55z^{8}\$Failed^{-1}-16z^{8}\$Failed^{-1}+5z^{8}\$Failed^{-1}-16z^{7}\$Failed^{-1}-10z^{7}\$Failed^{-1}-3z^{7}\$Failed^{-1}-22z^{7}\$Failed^{-1}-12z^{7}\$Failed^{-1}+z^{7}\$Failed^{-1}-4z^{6}\$Failed^{-1}+31z^{6}\$Failed^{-1}+70z^{6}\$Failed^{-1}+44z^{6}\$Failed^{-1}+13z^{6}\$Failed^{-1}+4z^{6}\$Failed^{-1}+20z^{5}\$Failed^{-1}+25z^{5}\$Failed^{-1}+10z^{5}\$Failed^{-1}+9z^{5}\$Failed^{-1}+13z^{5}\$Failed^{-1}+9z^{5}\$Failed^{-1}+5z^{4}\$Failed^{-1}-17z^{4}\$Failed^{-1}-30z^{4}\$Failed^{-1}-12z^{4}\$Failed^{-1}-13z^{4}\$Failed^{-1}-6z^{4}\$Failed^{-1}+3z^{4}\$Failed^{-1}-8z^{3}\$Failed^{-1}-9z^{3}\$Failed^{-1}+11z^{3}\$Failed^{-1}+10z^{3}\$Failed^{-1}-10z^{3}\$Failed^{-1}-8z^{3}\$Failed^{-1}-2z^{2}\$Failed^{-1}+7z^{2}\$Failed^{-1}+2z^{2}\$Failed^{-1}-5z^{2}\$Failed^{-1}+4z^{2}\$Failed^{-1}+z^{2}\$Failed^{-1}-z^{2}\$Failed^{-1}-7z\$Failed^{-1}-6z\$Failed^{-1}+2z\$Failed^{-1}+z\$Failed^{-1}-2\$Failed^{-1}+2\$Failed^{-1}+4\$Failed^{-1}+\$Failed^{-1}}
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