K14a5799
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
4 10 20 18 2 8 22 24 26 28 12 16 14 6
Notes on presentations of K14a5799
Polynomial invariants
Jones polynomial
Data:K14a5799/Jones Polynomial
Alexander polynomial
4
t
4
−
20
t
3
+
49
t
2
−
76
t
+
87
−
76
t
−
1
+
49
t
−
2
−
20
t
−
3
+
4
t
−
4
{\displaystyle 4t^{4}-20t^{3}+49t^{2}-76t+87-76t^{-1}+49t^{-2}-20t^{-3}+4t^{-4}}
Conway polynomial
Data:K14a5799/Conway Polynomial
Determinant
Data:K14a5799/Determinant
Signature
Data:K14a5799/Signature
HOMFLY-PT polynomial
z
8
a
−
4
+
2
z
8
a
−
6
+
z
8
a
−
8
−
z
6
a
−
2
+
3
z
6
a
−
4
+
8
z
6
a
−
6
+
3
z
6
a
−
8
−
z
6
a
−
10
−
3
z
4
a
−
2
+
3
z
4
a
−
4
+
11
z
4
a
−
6
+
z
4
a
−
8
−
3
z
4
a
−
10
−
2
z
2
a
−
2
+
3
z
2
a
−
4
+
8
z
2
a
−
6
−
4
z
2
a
−
8
−
z
2
a
−
10
+
a
−
4
+
3
a
−
6
−
4
a
−
8
+
a
−
10
{\displaystyle z^{8}a^{-4}+2z^{8}a^{-6}+z^{8}a^{-8}-z^{6}a^{-2}+3z^{6}a^{-4}+8z^{6}a^{-6}+3z^{6}a^{-8}-z^{6}a^{-10}-3z^{4}a^{-2}+3z^{4}a^{-4}+11z^{4}a^{-6}+z^{4}a^{-8}-3z^{4}a^{-10}-2z^{2}a^{-2}+3z^{2}a^{-4}+8z^{2}a^{-6}-4z^{2}a^{-8}-z^{2}a^{-10}+a^{-4}+3a^{-6}-4a^{-8}+a^{-10}}
Kauffman polynomial
2
z
13
$
F
a
i
l
e
d
−
1
+
2
z
13
$
F
a
i
l
e
d
−
1
+
6
z
12
$
F
a
i
l
e
d
−
1
+
12
z
12
$
F
a
i
l
e
d
−
1
+
6
z
12
$
F
a
i
l
e
d
−
1
+
10
z
11
$
F
a
i
l
e
d
−
1
+
11
z
11
$
F
a
i
l
e
d
−
1
+
9
z
11
$
F
a
i
l
e
d
−
1
+
8
z
11
$
F
a
i
l
e
d
−
1
+
11
z
10
$
F
a
i
l
e
d
−
1
−
z
10
$
F
a
i
l
e
d
−
1
−
31
z
10
$
F
a
i
l
e
d
−
1
−
11
z
10
$
F
a
i
l
e
d
−
1
+
8
z
10
$
F
a
i
l
e
d
−
1
+
8
z
9
$
F
a
i
l
e
d
−
1
−
19
z
9
$
F
a
i
l
e
d
−
1
−
36
z
9
$
F
a
i
l
e
d
−
1
−
32
z
9
$
F
a
i
l
e
d
−
1
−
16
z
9
$
F
a
i
l
e
d
−
1
+
7
z
9
$
F
a
i
l
e
d
−
1
+
4
z
8
$
F
a
i
l
e
d
−
1
−
29
z
8
$
F
a
i
l
e
d
−
1
−
27
z
8
$
F
a
i
l
e
d
−
1
+
48
z
8
$
F
a
i
l
e
d
−
1
+
22
z
8
$
F
a
i
l
e
d
−
1
−
16
z
8
$
F
a
i
l
e
d
−
1
+
4
z
8
$
F
a
i
l
e
d
−
1
+
z
7
$
F
a
i
l
e
d
−
1
−
22
z
7
$
F
a
i
l
e
d
−
1
+
2
z
7
$
F
a
i
l
e
d
−
1
+
43
z
7
$
F
a
i
l
e
d
−
1
+
54
z
7
$
F
a
i
l
e
d
−
1
+
15
z
7
$
F
a
i
l
e
d
−
1
−
20
z
7
$
F
a
i
l
e
d
−
1
+
z
7
$
F
a
i
l
e
d
−
1
−
12
z
6
$
F
a
i
l
e
d
−
1
+
25
z
6
$
F
a
i
l
e
d
−
1
+
47
z
6
$
F
a
i
l
e
d
−
1
−
40
z
6
$
F
a
i
l
e
d
−
1
−
34
z
6
$
F
a
i
l
e
d
−
1
+
3
z
6
$
F
a
i
l
e
d
−
1
−
13
z
6
$
F
a
i
l
e
d
−
1
−
3
z
5
$
F
a
i
l
e
d
−
1
+
17
z
5
$
F
a
i
l
e
d
−
1
+
17
z
5
$
F
a
i
l
e
d
−
1
−
16
z
5
$
F
a
i
l
e
d
−
1
−
44
z
5
$
F
a
i
l
e
d
−
1
−
11
z
5
$
F
a
i
l
e
d
−
1
+
17
z
5
$
F
a
i
l
e
d
−
1
−
3
z
5
$
F
a
i
l
e
d
−
1
+
10
z
4
$
F
a
i
l
e
d
−
1
−
11
z
4
$
F
a
i
l
e
d
−
1
−
33
z
4
$
F
a
i
l
e
d
−
1
+
14
z
4
$
F
a
i
l
e
d
−
1
+
23
z
4
$
F
a
i
l
e
d
−
1
+
9
z
4
$
F
a
i
l
e
d
−
1
+
12
z
4
$
F
a
i
l
e
d
−
1
+
2
z
3
$
F
a
i
l
e
d
−
1
−
6
z
3
$
F
a
i
l
e
d
−
1
−
13
z
3
$
F
a
i
l
e
d
−
1
−
2
z
3
$
F
a
i
l
e
d
−
1
+
10
z
3
$
F
a
i
l
e
d
−
1
+
z
3
$
F
a
i
l
e
d
−
1
−
4
z
3
$
F
a
i
l
e
d
−
1
+
2
z
3
$
F
a
i
l
e
d
−
1
−
3
z
2
$
F
a
i
l
e
d
−
1
+
13
z
2
$
F
a
i
l
e
d
−
1
+
6
z
2
$
F
a
i
l
e
d
−
1
−
7
z
2
$
F
a
i
l
e
d
−
1
−
5
z
2
$
F
a
i
l
e
d
−
1
−
2
z
2
$
F
a
i
l
e
d
−
1
+
z
$
F
a
i
l
e
d
−
1
+
z
$
F
a
i
l
e
d
−
1
+
3
z
$
F
a
i
l
e
d
−
1
+
3
z
$
F
a
i
l
e
d
−
1
+
$
F
a
i
l
e
d
−
1
−
3
$
F
a
i
l
e
d
−
1
−
4
$
F
a
i
l
e
d
−
1
−
$
F
a
i
l
e
d
−
1
{\displaystyle 2z^{13}\$Failed^{-1}+2z^{13}\$Failed^{-1}+6z^{12}\$Failed^{-1}+12z^{12}\$Failed^{-1}+6z^{12}\$Failed^{-1}+10z^{11}\$Failed^{-1}+11z^{11}\$Failed^{-1}+9z^{11}\$Failed^{-1}+8z^{11}\$Failed^{-1}+11z^{10}\$Failed^{-1}-z^{10}\$Failed^{-1}-31z^{10}\$Failed^{-1}-11z^{10}\$Failed^{-1}+8z^{10}\$Failed^{-1}+8z^{9}\$Failed^{-1}-19z^{9}\$Failed^{-1}-36z^{9}\$Failed^{-1}-32z^{9}\$Failed^{-1}-16z^{9}\$Failed^{-1}+7z^{9}\$Failed^{-1}+4z^{8}\$Failed^{-1}-29z^{8}\$Failed^{-1}-27z^{8}\$Failed^{-1}+48z^{8}\$Failed^{-1}+22z^{8}\$Failed^{-1}-16z^{8}\$Failed^{-1}+4z^{8}\$Failed^{-1}+z^{7}\$Failed^{-1}-22z^{7}\$Failed^{-1}+2z^{7}\$Failed^{-1}+43z^{7}\$Failed^{-1}+54z^{7}\$Failed^{-1}+15z^{7}\$Failed^{-1}-20z^{7}\$Failed^{-1}+z^{7}\$Failed^{-1}-12z^{6}\$Failed^{-1}+25z^{6}\$Failed^{-1}+47z^{6}\$Failed^{-1}-40z^{6}\$Failed^{-1}-34z^{6}\$Failed^{-1}+3z^{6}\$Failed^{-1}-13z^{6}\$Failed^{-1}-3z^{5}\$Failed^{-1}+17z^{5}\$Failed^{-1}+17z^{5}\$Failed^{-1}-16z^{5}\$Failed^{-1}-44z^{5}\$Failed^{-1}-11z^{5}\$Failed^{-1}+17z^{5}\$Failed^{-1}-3z^{5}\$Failed^{-1}+10z^{4}\$Failed^{-1}-11z^{4}\$Failed^{-1}-33z^{4}\$Failed^{-1}+14z^{4}\$Failed^{-1}+23z^{4}\$Failed^{-1}+9z^{4}\$Failed^{-1}+12z^{4}\$Failed^{-1}+2z^{3}\$Failed^{-1}-6z^{3}\$Failed^{-1}-13z^{3}\$Failed^{-1}-2z^{3}\$Failed^{-1}+10z^{3}\$Failed^{-1}+z^{3}\$Failed^{-1}-4z^{3}\$Failed^{-1}+2z^{3}\$Failed^{-1}-3z^{2}\$Failed^{-1}+13z^{2}\$Failed^{-1}+6z^{2}\$Failed^{-1}-7z^{2}\$Failed^{-1}-5z^{2}\$Failed^{-1}-2z^{2}\$Failed^{-1}+z\$Failed^{-1}+z\$Failed^{-1}+3z\$Failed^{-1}+3z\$Failed^{-1}+\$Failed^{-1}-3\$Failed^{-1}-4\$Failed^{-1}-\$Failed^{-1}}
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