 L11a326 |
 L11a328 |
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 Knotscape |
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The 2-Component Link L11a327Visit L11a327's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X10,1,11,2 X2,11,3,12 X12,3,13,4 X18,10,19,9 X6,13,7,14 X14,7,15,8 X8,15,1,16 X22,18,9,17 X16,22,17,21 X4,20,5,19 X20,6,21,5 |
| Gauss Code: | {{1, -2, 3, -10, 11, -5, 6, -7}, {4, -1, 2, -3, 5, -6, 7, -9, 8, -4, 10, -11, 9, -8}} |
| Jones Polynomial: | - q-13/2 + 2q-11/2 - 5q-9/2 + 9q-7/2 - 12q-5/2 + 13q-3/2 - 14q-1/2 + 11q1/2 - 9q3/2 + 5q5/2 - 2q7/2 + q9/2 |
| A2 (sl(3)) Invariant: | q-18 + 3q-14 - q-12 + q-10 + q-8 - 2q-6 + 4q-4 - q-2 + 5 + q2 + q6 - 3q8 - q12 |
| HOMFLY-PT Polynomial: | a-1z-1 + 10a-1z + 13a-1z3 + 6a-1z5 + a-1z7 - 3az-1 - 22az - 36az3 - 25az5 - 8az7 - az9 + 2a3z-1 + 10a3z + 13a3z3 + 6a3z5 + a3z7 |
| Kauffman Polynomial: | - 4a-4z2 + 4a-4z4 - a-4z6 - 4a-3z3 + 6a-3z5 - 2a-3z7 - a-2 + 7a-2z2 - 10a-2z4 + 9a-2z6 - 3a-2z8 + a-1z-1 - 12a-1z + 28a-1z3 - 21a-1z5 + 10a-1z7 - 3a-1z9 - 3 + 21z2 - 26z4 + 15z6 - 3z8 - z10 + 3az-1 - 24az + 47az3 - 43az5 + 21az7 - 6az9 - 3a2 + 18a2z2 - 30a2z4 + 17a2z6 - 4a2z8 - a2z10 + 2a3z-1 - 9a3z + 10a3z3 - 10a3z5 + 6a3z7 - 3a3z9 + 7a4z2 - 14a4z4 + 10a4z6 - 4a4z8 + a5z - 2a5z3 + 5a5z5 - 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, 327]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 327]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[18, 10, 19, 9], > X[6, 13, 7, 14], X[14, 7, 15, 8], X[8, 15, 1, 16], X[22, 18, 9, 17], > X[16, 22, 17, 21], X[4, 20, 5, 19], X[20, 6, 21, 5]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -10, 11, -5, 6, -7},
> {4, -1, 2, -3, 5, -6, 7, -9, 8, -4, 10, -11, 9, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 2 5 9 12 13 14 3/2
-q + ----- - ---- + ---- - ---- + ---- - ------- + 11 Sqrt[q] - 9 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 -12 -10 -8 2 4 -2 2 6 8 12
5 + q + --- - q + q + q - -- + -- - q + q + q - 3 q - q
14 6 4
q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 327]][a, z] |
Out[8]= | 3 3
1 3 a 2 a 10 z 3 13 z 3 3 3
--- - --- + ---- + ---- - 22 a z + 10 a z + ----- - 36 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, 327]][a, z] |
Out[9]= | 3
-2 2 1 3 a 2 a 12 z 3 5 7
-3 - a - 3 a + --- + --- + ---- - ---- - 24 a z - 9 a z + a z - 2 a z +
a z z z a
2 2 3 3
2 4 z 7 z 2 2 4 2 6 2 4 z 28 z 3
> 21 z - ---- + ---- + 18 a z + 7 a z - a z - ---- + ----- + 47 a z +
4 2 3 a
a a a
4 4
3 3 5 3 7 3 4 4 z 10 z 2 4 4 4
> 10 a z - 2 a z + 3 a z - 26 z + ---- - ----- - 30 a z - 14 a z +
4 2
a a
5 5
6 4 6 z 21 z 5 3 5 5 5 7 5 6
> 4 a z + ---- - ----- - 43 a z - 10 a z + 5 a z - a z + 15 z -
3 a
a
6 6 7 7
z 9 z 2 6 4 6 6 6 2 z 10 z 7
> -- + ---- + 17 a z + 10 a z - 2 a z - ---- + ----- + 21 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
> 6 a z - 3 a z - 3 z - ---- - 4 a z - 4 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 1 4 2 6 3 6
8 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
2 14 6 12 5 10 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
6 7 6 2 2 2 4 2 4 3 6 3
> ----- + ---- + ---- + 5 t + 6 q t + 4 q t + 5 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 L11a327 |
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