K14n26370
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
6 -14 20 18 22 16 -2 24 26 28 4 10 12 8
Notes on presentations of K14n26370
Polynomial invariants
Jones polynomial
Data:K14n26370/Jones Polynomial
Alexander polynomial
−
2
t
4
+
15
t
3
−
47
t
2
+
85
t
−
101
+
85
t
−
1
−
47
t
−
2
+
15
t
−
3
−
2
t
−
4
{\displaystyle -2t^{4}+15t^{3}-47t^{2}+85t-101+85t^{-1}-47t^{-2}+15t^{-3}-2t^{-4}}
Conway polynomial
Data:K14n26370/Conway Polynomial
Determinant
Data:K14n26370/Determinant
Signature
Data:K14n26370/Signature
HOMFLY-PT polynomial
−
z
4
a
8
−
2
z
2
a
8
+
3
z
6
a
6
+
8
z
4
a
6
+
6
z
2
a
6
+
a
6
−
2
z
8
a
4
−
8
z
6
a
4
−
13
z
4
a
4
−
10
z
2
a
4
−
3
a
4
+
4
z
6
a
2
+
11
z
4
a
2
+
9
z
2
a
2
+
3
a
2
−
2
z
4
−
3
z
2
{\displaystyle -z^{4}a^{8}-2z^{2}a^{8}+3z^{6}a^{6}+8z^{4}a^{6}+6z^{2}a^{6}+a^{6}-2z^{8}a^{4}-8z^{6}a^{4}-13z^{4}a^{4}-10z^{2}a^{4}-3a^{4}+4z^{6}a^{2}+11z^{4}a^{2}+9z^{2}a^{2}+3a^{2}-2z^{4}-3z^{2}}
Kauffman polynomial
5
a
6
z
12
+
5
a
4
z
12
+
14
a
7
z
11
+
28
a
5
z
11
+
14
a
3
z
11
+
17
a
8
z
10
+
25
a
6
z
10
+
22
a
4
z
10
+
14
a
2
z
10
+
12
a
9
z
9
−
13
a
7
z
9
−
55
a
5
z
9
−
24
a
3
z
9
+
6
a
z
9
+
5
a
10
z
8
−
34
a
8
z
8
−
81
a
6
z
8
−
70
a
4
z
8
−
27
a
2
z
8
+
z
8
+
a
11
z
7
−
27
a
9
z
7
−
23
a
7
z
7
+
36
a
5
z
7
+
34
a
3
z
7
+
3
a
z
7
−
11
a
10
z
6
+
16
a
8
z
6
+
70
a
6
z
6
+
78
a
4
z
6
+
45
a
2
z
6
+
10
z
6
−
2
a
11
z
5
+
20
a
9
z
5
+
25
a
7
z
5
−
17
a
5
z
5
−
30
a
3
z
5
−
7
a
z
5
+
3
z
5
a
−
1
+
8
a
10
z
4
−
31
a
6
z
4
−
46
a
4
z
4
−
38
a
2
z
4
−
15
z
4
+
a
11
z
3
−
6
a
9
z
3
−
12
a
7
z
3
+
a
5
z
3
+
12
a
3
z
3
+
3
a
z
3
−
3
z
3
a
−
1
−
2
a
10
z
2
−
2
a
8
z
2
+
6
a
6
z
2
+
15
a
4
z
2
+
15
a
2
z
2
+
6
z
2
+
a
9
z
+
4
a
7
z
+
4
a
5
z
−
a
z
−
a
6
−
3
a
4
−
3
a
2
{\displaystyle 5a^{6}z^{12}+5a^{4}z^{12}+14a^{7}z^{11}+28a^{5}z^{11}+14a^{3}z^{11}+17a^{8}z^{10}+25a^{6}z^{10}+22a^{4}z^{10}+14a^{2}z^{10}+12a^{9}z^{9}-13a^{7}z^{9}-55a^{5}z^{9}-24a^{3}z^{9}+6az^{9}+5a^{10}z^{8}-34a^{8}z^{8}-81a^{6}z^{8}-70a^{4}z^{8}-27a^{2}z^{8}+z^{8}+a^{11}z^{7}-27a^{9}z^{7}-23a^{7}z^{7}+36a^{5}z^{7}+34a^{3}z^{7}+3az^{7}-11a^{10}z^{6}+16a^{8}z^{6}+70a^{6}z^{6}+78a^{4}z^{6}+45a^{2}z^{6}+10z^{6}-2a^{11}z^{5}+20a^{9}z^{5}+25a^{7}z^{5}-17a^{5}z^{5}-30a^{3}z^{5}-7az^{5}+3z^{5}a^{-1}+8a^{10}z^{4}-31a^{6}z^{4}-46a^{4}z^{4}-38a^{2}z^{4}-15z^{4}+a^{11}z^{3}-6a^{9}z^{3}-12a^{7}z^{3}+a^{5}z^{3}+12a^{3}z^{3}+3az^{3}-3z^{3}a^{-1}-2a^{10}z^{2}-2a^{8}z^{2}+6a^{6}z^{2}+15a^{4}z^{2}+15a^{2}z^{2}+6z^{2}+a^{9}z+4a^{7}z+4a^{5}z-az-a^{6}-3a^{4}-3a^{2}}
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