K14a11714
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
4 16 10 12 22 6 20 24 2 26 8 28 18 14
Notes on presentations of K14a11714
Polynomial invariants
Jones polynomial
Data:K14a11714/Jones Polynomial
Alexander polynomial
t
5
−
8
t
4
+
28
t
3
−
57
t
2
+
84
t
−
95
+
84
t
−
1
−
57
t
−
2
+
28
t
−
3
−
8
t
−
4
+
t
−
5
{\displaystyle t^{5}-8t^{4}+28t^{3}-57t^{2}+84t-95+84t^{-1}-57t^{-2}+28t^{-3}-8t^{-4}+t^{-5}}
Conway polynomial
Data:K14a11714/Conway Polynomial
Determinant
Data:K14a11714/Determinant
Signature
Data:K14a11714/Signature
HOMFLY-PT polynomial
−
z
4
a
12
−
3
z
2
a
12
−
2
a
12
+
3
z
6
a
10
+
12
z
4
a
10
+
14
z
2
a
10
+
5
a
10
−
3
z
8
a
8
−
15
z
6
a
8
−
26
z
4
a
8
−
19
z
2
a
8
−
5
a
8
+
z
10
a
6
+
6
z
8
a
6
+
15
z
6
a
6
+
20
z
4
a
6
+
12
z
2
a
6
+
a
6
−
z
8
a
4
−
4
z
6
a
4
−
4
z
4
a
4
+
z
2
a
4
+
2
a
4
{\displaystyle -z^{4}a^{12}-3z^{2}a^{12}-2a^{12}+3z^{6}a^{10}+12z^{4}a^{10}+14z^{2}a^{10}+5a^{10}-3z^{8}a^{8}-15z^{6}a^{8}-26z^{4}a^{8}-19z^{2}a^{8}-5a^{8}+z^{10}a^{6}+6z^{8}a^{6}+15z^{6}a^{6}+20z^{4}a^{6}+12z^{2}a^{6}+a^{6}-z^{8}a^{4}-4z^{6}a^{4}-4z^{4}a^{4}+z^{2}a^{4}+2a^{4}}
Kauffman polynomial
z
5
a
17
−
z
3
a
17
+
4
z
6
a
16
−
3
z
4
a
16
+
10
z
7
a
15
−
11
z
5
a
15
+
6
z
3
a
15
−
z
a
15
+
18
z
8
a
14
−
27
z
6
a
14
+
20
z
4
a
14
−
5
z
2
a
14
+
25
z
9
a
13
−
46
z
7
a
13
+
37
z
5
a
13
−
15
z
3
a
13
+
3
z
a
13
+
27
z
10
a
12
−
54
z
8
a
12
+
40
z
6
a
12
−
23
z
4
a
12
+
11
z
2
a
12
−
2
a
12
+
21
z
11
a
11
−
29
z
9
a
11
−
26
z
7
a
11
+
51
z
5
a
11
−
28
z
3
a
11
+
4
z
a
11
+
10
z
12
a
10
+
18
z
10
a
10
−
136
z
8
a
10
+
192
z
6
a
10
−
131
z
4
a
10
+
44
z
2
a
10
−
5
a
10
+
2
z
13
a
9
+
37
z
11
a
9
−
139
z
9
a
9
+
147
z
7
a
9
−
64
z
5
a
9
+
16
z
3
a
9
−
3
z
a
9
+
17
z
12
a
8
−
22
z
10
a
8
−
99
z
8
a
8
+
218
z
6
a
8
−
160
z
4
a
8
+
52
z
2
a
8
−
5
a
8
+
2
z
13
a
7
+
25
z
11
a
7
−
123
z
9
a
7
+
169
z
7
a
7
−
93
z
5
a
7
+
29
z
3
a
7
−
6
z
a
7
+
7
z
12
a
6
−
8
z
10
a
6
−
58
z
8
a
6
+
134
z
6
a
6
−
99
z
4
a
6
+
27
z
2
a
6
−
a
6
+
9
z
11
a
5
−
37
z
9
a
5
+
48
z
7
a
5
−
22
z
5
a
5
+
5
z
3
a
5
−
3
z
a
5
+
5
z
10
a
4
−
23
z
8
a
4
+
37
z
6
a
4
−
24
z
4
a
4
+
3
z
2
a
4
+
2
a
4
+
z
9
a
3
−
4
z
7
a
3
+
5
z
5
a
3
−
2
z
3
a
3
{\displaystyle z^{5}a^{17}-z^{3}a^{17}+4z^{6}a^{16}-3z^{4}a^{16}+10z^{7}a^{15}-11z^{5}a^{15}+6z^{3}a^{15}-za^{15}+18z^{8}a^{14}-27z^{6}a^{14}+20z^{4}a^{14}-5z^{2}a^{14}+25z^{9}a^{13}-46z^{7}a^{13}+37z^{5}a^{13}-15z^{3}a^{13}+3za^{13}+27z^{10}a^{12}-54z^{8}a^{12}+40z^{6}a^{12}-23z^{4}a^{12}+11z^{2}a^{12}-2a^{12}+21z^{11}a^{11}-29z^{9}a^{11}-26z^{7}a^{11}+51z^{5}a^{11}-28z^{3}a^{11}+4za^{11}+10z^{12}a^{10}+18z^{10}a^{10}-136z^{8}a^{10}+192z^{6}a^{10}-131z^{4}a^{10}+44z^{2}a^{10}-5a^{10}+2z^{13}a^{9}+37z^{11}a^{9}-139z^{9}a^{9}+147z^{7}a^{9}-64z^{5}a^{9}+16z^{3}a^{9}-3za^{9}+17z^{12}a^{8}-22z^{10}a^{8}-99z^{8}a^{8}+218z^{6}a^{8}-160z^{4}a^{8}+52z^{2}a^{8}-5a^{8}+2z^{13}a^{7}+25z^{11}a^{7}-123z^{9}a^{7}+169z^{7}a^{7}-93z^{5}a^{7}+29z^{3}a^{7}-6za^{7}+7z^{12}a^{6}-8z^{10}a^{6}-58z^{8}a^{6}+134z^{6}a^{6}-99z^{4}a^{6}+27z^{2}a^{6}-a^{6}+9z^{11}a^{5}-37z^{9}a^{5}+48z^{7}a^{5}-22z^{5}a^{5}+5z^{3}a^{5}-3za^{5}+5z^{10}a^{4}-23z^{8}a^{4}+37z^{6}a^{4}-24z^{4}a^{4}+3z^{2}a^{4}+2a^{4}+z^{9}a^{3}-4z^{7}a^{3}+5z^{5}a^{3}-2z^{3}a^{3}}
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