 L11a286 |
 L11a288 |
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 Knotscape |
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The 2-Component Link L11a287Visit L11a287's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X10,1,11,2 X12,4,13,3 X16,9,17,10 X20,12,21,11 X22,15,9,16 X14,6,15,5 X18,8,19,7 X4,14,5,13 X6,18,7,17 X8,20,1,19 X2,21,3,22 |
| Gauss Code: | {{1, -11, 2, -8, 6, -9, 7, -10}, {3, -1, 4, -2, 8, -6, 5, -3, 9, -7, 10, -4, 11, -5}} |
| Jones Polynomial: | - q-5/2 + 3q-3/2 - 6q-1/2 + 10q1/2 - 14q3/2 + 15q5/2 - 16q7/2 + 14q9/2 - 11q11/2 + 6q13/2 - 3q15/2 + q17/2 |
| A2 (sl(3)) Invariant: | q-6 - q-4 + 2q-2 - 2 + q4 - 2q6 + 5q8 - 2q10 + 4q12 + q14 + q16 + 3q18 - 2q20 + q22 - q24 |
| HOMFLY-PT Polynomial: | - a-5z-1 + 3a-5z + 8a-5z3 + 5a-5z5 + a-5z7 + a-3z-1 - 5a-3z - 19a-3z3 - 18a-3z5 - 7a-3z7 - a-3z9 + 4a-1z + 8a-1z3 + 5a-1z5 + a-1z7 |
| Kauffman Polynomial: | a-10z2 - a-10z4 - a-9z + 3a-9z3 - 3a-9z5 - a-8z2 + 4a-8z4 - 5a-8z6 - a-7z - 5a-7z3 + 9a-7z5 - 7a-7z7 - 2a-6z2 - 4a-6z4 + 10a-6z6 - 7a-6z8 - a-5z-1 + a-5z3 + 6a-5z7 - 5a-5z9 + a-4 - 7a-4z4 + 14a-4z6 - 3a-4z8 - 2a-4z10 - a-3z-1 - 5a-3z + 26a-3z3 - 35a-3z5 + 29a-3z7 - 9a-3z9 + 4a-2z2 - 12a-2z4 + 11a-2z6 + a-2z8 - 2a-2z10 - 5a-1z + 13a-1z3 - 19a-1z5 + 15a-1z7 - 4a-1z9 + 4z2 - 14z4 + 12z6 - 3z8 - 4az3 + 4az5 - az7 |
| 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, 287]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 287]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 4, 13, 3], X[16, 9, 17, 10], X[20, 12, 21, 11], > X[22, 15, 9, 16], X[14, 6, 15, 5], X[18, 8, 19, 7], X[4, 14, 5, 13], > X[6, 18, 7, 17], X[8, 20, 1, 19], X[2, 21, 3, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 2, -8, 6, -9, 7, -10},
> {3, -1, 4, -2, 8, -6, 5, -3, 9, -7, 10, -4, 11, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 3 6 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 14 q + 15 q - 16 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 14 q - 11 q + 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -6 -4 2 4 6 8 10 12 14 16 18
-2 + q - q + -- + q - 2 q + 5 q - 2 q + 4 q + q + q + 3 q -
2
q
20 22 24
> 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 287]][a, z] |
Out[8]= | 3 3 3 5 5 5
1 1 3 z 5 z 4 z 8 z 19 z 8 z 5 z 18 z 5 z
-(----) + ---- + --- - --- + --- + ---- - ----- + ---- + ---- - ----- + ---- +
5 3 5 3 a 5 3 a 5 3 a
a z a z a a a a a a
7 7 7 9
z 7 z z z
> -- - ---- + -- - --
5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 287]][a, z] |
Out[9]= | 2 2 2 2
-4 1 1 z z 5 z 5 z 2 z z 2 z 4 z
a - ---- - ---- - -- - -- - --- - --- + 4 z + --- - -- - ---- + ---- +
5 3 9 7 3 a 10 8 6 2
a z a z a a a a a a a
3 3 3 3 3 4 4 4
3 z 5 z z 26 z 13 z 3 4 z 4 z 4 z
> ---- - ---- + -- + ----- + ----- - 4 a z - 14 z - --- + ---- - ---- -
9 7 5 3 a 10 8 6
a a a a a a a
4 4 5 5 5 5 6
7 z 12 z 3 z 9 z 35 z 19 z 5 6 5 z
> ---- - ----- - ---- + ---- - ----- - ----- + 4 a z + 12 z - ---- +
4 2 9 7 3 a 8
a a a a a a
6 6 6 7 7 7 7 8
10 z 14 z 11 z 7 z 6 z 29 z 15 z 7 8 7 z
> ----- + ----- + ----- - ---- + ---- + ----- + ----- - a z - 3 z - ---- -
6 4 2 7 5 3 a 6
a a a a a a a
8 8 9 9 9 10 10
3 z z 5 z 9 z 4 z 2 z 2 z
> ---- + -- - ---- - ---- - ---- - ----- - -----
4 2 5 3 a 4 2
a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 2 1 2 4 6 4 q 4 6
8 q + 7 q + ----- + ----- + ----- + -- + ----- + - + ---- + 8 q t + 7 q t +
6 4 4 3 2 3 2 2 2 t t
q t q t q t t q t
6 2 8 2 8 3 10 3 10 4 12 4 12 5
> 8 q t + 8 q t + 6 q t + 8 q t + 5 q t + 7 q t + 2 q t +
14 5 14 6 16 6 18 7
> 4 q t + q t + 2 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a287 |
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