 L11a163 |
 L11a165 |
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The 2-Component Link L11a164Visit L11a164's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X8192 X2,9,3,10 X10,3,11,4 X14,5,15,6 X20,16,21,15 X18,12,19,11 X12,20,13,19 X22,18,7,17 X16,22,17,21 X6718 X4,13,5,14 |
| Gauss Code: | {{1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, 6, -7, 11, -4, 5, -9, 8, -6, 7, -5, 9, -8}} |
| Jones Polynomial: | - q-13/2 + 2q-11/2 - 5q-9/2 + 8q-7/2 - 11q-5/2 + 12q-3/2 - 13q-1/2 + 10q1/2 - 8q3/2 + 5q5/2 - 2q7/2 + q9/2 |
| A2 (sl(3)) Invariant: | q-18 + 3q-14 + 2q-10 + 2q-8 - q-6 + 4q-4 - q-2 + 4 - q4 - 3q8 - q12 |
| HOMFLY-PT Polynomial: | 2a-1z-1 + 11a-1z + 13a-1z3 + 6a-1z5 + a-1z7 - 5az-1 - 25az - 37az3 - 25az5 - 8az7 - az9 + 3a3z-1 + 11a3z + 13a3z3 + 6a3z5 + a3z7 |
| Kauffman Polynomial: | a-4 - 4a-4z2 + 4a-4z4 - a-4z6 - 3a-3z3 + 6a-3z5 - 2a-3z7 + 3a-2z2 - 7a-2z4 + 9a-2z6 - 3a-2z8 + 2a-1z-1 - 11a-1z + 19a-1z3 - 16a-1z5 + 10a-1z7 - 3a-1z9 - 5 + 27z2 - 37z4 + 20z6 - 3z8 - z10 + 5az-1 - 28az + 51az3 - 49az5 + 24az7 - 6az9 - 5a2 + 23a2z2 - 34a2z4 + 17a2z6 - 3a2z8 - a2z10 + 3a3z-1 - 13a3z + 22a3z3 - 20a3z5 + 9a3z7 - 3a3z9 + 2a4z2 - 4a4z4 + 5a4z6 - 3a4z8 + 2a5z - 4a5z3 + 6a5z5 - 3a5z7 - a6z2 + 4a6z4 - 2a6z6 - 2a7z + 3a7z3 - a7z5 |
| Khovanov Homology: |
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Computer Talk. The data above can be recomputed by Mathematica using the package KnotTheory`. Following setup, the sample Mathematica session below reproduces most of the above data (Mathematica system prompts in blue, human input in red, Mathematica output in black):
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... | |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 164]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 164]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[14, 5, 15, 6], > X[20, 16, 21, 15], X[18, 12, 19, 11], X[12, 20, 13, 19], X[22, 18, 7, 17], > X[16, 22, 17, 21], X[6, 7, 1, 8], X[4, 13, 5, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -11, 4, -10},
> {10, -1, 2, -3, 6, -7, 11, -4, 5, -9, 8, -6, 7, -5, 9, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 2 5 8 11 12 13 3/2
-q + ----- - ---- + ---- - ---- + ---- - ------- + 10 Sqrt[q] - 8 q +
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
5/2 7/2 9/2
> 5 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 3 2 2 -6 4 -2 4 8 12
4 + q + --- + --- + -- - q + -- - q - q - 3 q - q
14 10 8 4
q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 164]][a, z] |
Out[8]= | 3 3
2 5 a 3 a 11 z 3 13 z 3 3 3
--- - --- + ---- + ---- - 25 a z + 11 a z + ----- - 37 a z + 13 a z +
a z z z a a
5 7
6 z 5 3 5 z 7 3 7 9
> ---- - 25 a z + 6 a z + -- - 8 a z + a z - a z
a a |
In[9]:= | Kauffman[Link[11, Alternating, 164]][a, z] |
Out[9]= | 3
-4 2 2 5 a 3 a 11 z 3 5
-5 + a - 5 a + --- + --- + ---- - ---- - 28 a z - 13 a z + 2 a z -
a z z z a
2 2 3 3
7 2 4 z 3 z 2 2 4 2 6 2 3 z 19 z
> 2 a z + 27 z - ---- + ---- + 23 a z + 2 a z - a z - ---- + ----- +
4 2 3 a
a a a
4 4
3 3 3 5 3 7 3 4 4 z 7 z 2 4
> 51 a z + 22 a z - 4 a z + 3 a z - 37 z + ---- - ---- - 34 a z -
4 2
a a
5 5
4 4 6 4 6 z 16 z 5 3 5 5 5 7 5
> 4 a z + 4 a z + ---- - ----- - 49 a z - 20 a z + 6 a z - a z +
3 a
a
6 6 7 7
6 z 9 z 2 6 4 6 6 6 2 z 10 z 7
> 20 z - -- + ---- + 17 a z + 5 a z - 2 a z - ---- + ----- + 24 a z +
4 2 3 a
a a a
8 9
3 7 5 7 8 3 z 2 8 4 8 3 z 9
> 9 a z - 3 a z - 3 z - ---- - 3 a z - 3 a z - ---- - 6 a z -
2 a
a
3 9 10 2 10
> 3 a z - z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 7 1 1 2 3 2 5 3 6
7 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
2 14 6 12 6 12 5 10 4 8 4 8 3 6 3 6 2
q q t q t q t q t q t q t q t q t
5 6 6 2 2 2 4 2 4 3 6 3
> ----- + ---- + ---- + 4 t + 6 q t + 4 q t + 4 q t + q t + 4 q t +
4 2 4 2
q t q t q t
6 4 8 4 10 5
> q t + q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a164 |
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