K12a25
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
4 8 10 16 2 20 22 18 6 14 24 12
Notes on presentations of K12a25
Polynomial invariants
Jones polynomial
q
6
−
5
q
5
+
11
q
4
−
17
q
3
+
24
q
2
−
28
q
+
29
−
26
q
−
1
+
20
q
−
2
−
13
q
−
3
+
7
q
−
4
−
3
q
−
5
+
q
−
6
{\displaystyle q^{6}-5q^{5}+11q^{4}-17q^{3}+24q^{2}-28q+29-26q^{-1}+20q^{-2}-13q^{-3}+7q^{-4}-3q^{-5}+q^{-6}}
Alexander polynomial
−
2
t
3
+
15
t
2
−
44
t
+
63
−
44
t
−
1
+
15
t
−
2
−
2
t
−
3
{\displaystyle -2t^{3}+15t^{2}-44t+63-44t^{-1}+15t^{-2}-2t^{-3}}
Conway polynomial
−
2
z
6
+
3
z
4
−
2
z
2
+
1
{\displaystyle -2z^{6}+3z^{4}-2z^{2}+1}
Determinant
185
Signature
0
HOMFLY-PT polynomial
a
6
−
3
z
2
a
4
−
2
a
4
+
3
z
4
a
2
+
3
z
2
a
2
+
2
a
2
−
z
6
−
z
2
−
1
−
z
6
a
−
2
−
z
4
a
−
2
−
z
2
a
−
2
+
a
−
2
+
z
4
a
−
4
{\displaystyle a^{6}-3z^{2}a^{4}-2a^{4}+3z^{4}a^{2}+3z^{2}a^{2}+2a^{2}-z^{6}-z^{2}-1-z^{6}a^{-2}-z^{4}a^{-2}-z^{2}a^{-2}+a^{-2}+z^{4}a^{-4}}
Kauffman polynomial
a
z
11
+
z
11
a
−
1
+
3
a
2
z
10
+
5
z
10
a
−
2
+
8
z
10
+
4
a
3
z
9
+
11
a
z
9
+
17
z
9
a
−
1
+
10
z
9
a
−
3
+
4
a
4
z
8
+
4
a
2
z
8
+
7
z
8
a
−
2
+
10
z
8
a
−
4
−
3
z
8
+
3
a
5
z
7
−
22
a
z
7
−
41
z
7
a
−
1
−
17
z
7
a
−
3
+
5
z
7
a
−
5
+
a
6
z
6
−
5
a
4
z
6
−
11
a
2
z
6
−
37
z
6
a
−
2
−
22
z
6
a
−
4
+
z
6
a
−
6
−
19
z
6
−
8
a
5
z
5
−
12
a
3
z
5
+
16
a
z
5
+
31
z
5
a
−
1
+
2
z
5
a
−
3
−
9
z
5
a
−
5
−
3
a
6
z
4
−
4
a
4
z
4
+
3
a
2
z
4
+
32
z
4
a
−
2
+
11
z
4
a
−
4
−
z
4
a
−
6
+
24
z
4
+
7
a
5
z
3
+
10
a
3
z
3
−
4
a
z
3
−
6
z
3
a
−
1
+
3
z
3
a
−
3
+
2
z
3
a
−
5
+
3
a
6
z
2
+
7
a
4
z
2
+
3
a
2
z
2
−
6
z
2
a
−
2
−
z
2
a
−
4
−
6
z
2
−
2
a
5
z
−
2
a
3
z
−
a
6
−
2
a
4
−
2
a
2
−
a
−
2
−
1
{\displaystyle az^{11}+z^{11}a^{-1}+3a^{2}z^{10}+5z^{10}a^{-2}+8z^{10}+4a^{3}z^{9}+11az^{9}+17z^{9}a^{-1}+10z^{9}a^{-3}+4a^{4}z^{8}+4a^{2}z^{8}+7z^{8}a^{-2}+10z^{8}a^{-4}-3z^{8}+3a^{5}z^{7}-22az^{7}-41z^{7}a^{-1}-17z^{7}a^{-3}+5z^{7}a^{-5}+a^{6}z^{6}-5a^{4}z^{6}-11a^{2}z^{6}-37z^{6}a^{-2}-22z^{6}a^{-4}+z^{6}a^{-6}-19z^{6}-8a^{5}z^{5}-12a^{3}z^{5}+16az^{5}+31z^{5}a^{-1}+2z^{5}a^{-3}-9z^{5}a^{-5}-3a^{6}z^{4}-4a^{4}z^{4}+3a^{2}z^{4}+32z^{4}a^{-2}+11z^{4}a^{-4}-z^{4}a^{-6}+24z^{4}+7a^{5}z^{3}+10a^{3}z^{3}-4az^{3}-6z^{3}a^{-1}+3z^{3}a^{-3}+2z^{3}a^{-5}+3a^{6}z^{2}+7a^{4}z^{2}+3a^{2}z^{2}-6z^{2}a^{-2}-z^{2}a^{-4}-6z^{2}-2a^{5}z-2a^{3}z-a^{6}-2a^{4}-2a^{2}-a^{-2}-1}
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