 L11a59 |
 L11a61 |
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 Knotscape |
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The 2-Component Link L11a60Visit L11a60's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X12,3,13,4 X14,8,15,7 X20,18,21,17 X18,9,19,10 X8,19,9,20 X22,16,5,15 X16,22,17,21 X10,14,11,13 X2536 X4,11,1,12 |
| Gauss Code: | {{1, -10, 2, -11}, {10, -1, 3, -6, 5, -9, 11, -2, 9, -3, 7, -8, 4, -5, 6, -4, 8, -7}} |
| Jones Polynomial: | - q-13/2 + 2q-11/2 - 6q-9/2 + 9q-7/2 - 13q-5/2 + 16q-3/2 - 16q-1/2 + 14q1/2 - 11q3/2 + 7q5/2 - 4q7/2 + q9/2 |
| A2 (sl(3)) Invariant: | q-22 + 2q-20 + 2q-16 + 4q-14 - 2q-12 + q-10 - 4q-6 + q-4 - 2q-2 + 3 + q2 - q4 + 4q6 - 2q8 + 2q12 - q14 |
| HOMFLY-PT Polynomial: | a-3z3 - a-1z-1 - 2a-1z - a-1z3 - a-1z5 + 2az-1 + 2az + az3 - az5 - a3z-1 + a3z + 3a3z3 - a5z-1 - 3a5z + a7z-1 |
| Kauffman Polynomial: | 2a-4z4 - a-4z6 - 6a-3z3 + 11a-3z5 - 4a-3z7 + 2a-2z2 - 12a-2z4 + 17a-2z6 - 6a-2z8 - a-1z-1 + 5a-1z - 12a-1z3 + 8a-1z5 + 5a-1z7 - 4a-1z9 - 1 + 6z2 - 21z4 + 25z6 - 8z8 - z10 - 2az-1 + 12az - 18az3 + 5az5 + 8az7 - 6az9 - 3a2 + 6a2z2 - 9a2z4 + 10a2z6 - 5a2z8 - a2z10 - a3z-1 + 8a3z - 14a3z3 + 12a3z5 - 4a3z7 - 2a3z9 - 2a4 + 2a4z2 + a4z4 + a4z6 - 3a4z8 + a5z-1 - 2a5z + a5z3 + 3a5z5 - 3a5z7 - a6 + 3a6z4 - 2a6z6 + a7z-1 - 3a7z + 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, 60]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 60]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[14, 8, 15, 7], X[20, 18, 21, 17], > X[18, 9, 19, 10], X[8, 19, 9, 20], X[22, 16, 5, 15], X[16, 22, 17, 21], > X[10, 14, 11, 13], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -6, 5, -9, 11, -2, 9, -3, 7, -8, 4, -5,
> 6, -4, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 2 6 9 13 16 16
-q + ----- - ---- + ---- - ---- + ---- - ------- + 14 Sqrt[q] -
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
3/2 5/2 7/2 9/2
> 11 q + 7 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -22 2 2 4 2 -10 4 -4 2 2 4 6
3 + q + --- + --- + --- - --- + q - -- + q - -- + q - q + 4 q -
20 16 14 12 6 2
q q q q q q
8 12 14
> 2 q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 60]][a, z] |
Out[8]= | 3 5 7 3 3
1 2 a a a a 2 z 3 5 z z 3
-(---) + --- - -- - -- + -- - --- + 2 a z + a z - 3 a z + -- - -- + a z +
a z z z z z a 3 a
a
5
3 3 z 5
> 3 a z - -- - a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 60]][a, z] |
Out[9]= | 3 5 7
2 4 6 1 2 a a a a 5 z 3
-1 - 3 a - 2 a - a - --- - --- - -- + -- + -- + --- + 12 a z + 8 a z -
a z z z z z a
2 3 3
5 7 2 2 z 2 2 4 2 6 z 12 z
> 2 a z - 3 a z + 6 z + ---- + 6 a z + 2 a z - ---- - ----- -
2 3 a
a a
4 4
3 3 3 5 3 7 3 4 2 z 12 z 2 4
> 18 a z - 14 a z + a z + 3 a z - 21 z + ---- - ----- - 9 a z +
4 2
a a
5 5
4 4 6 4 11 z 8 z 5 3 5 5 5 7 5
> a z + 3 a z + ----- + ---- + 5 a z + 12 a z + 3 a z - a z +
3 a
a
6 6 7 7
6 z 17 z 2 6 4 6 6 6 4 z 5 z 7
> 25 z - -- + ----- + 10 a z + a z - 2 a z - ---- + ---- + 8 a z -
4 2 3 a
a a a
8 9
3 7 5 7 8 6 z 2 8 4 8 4 z 9
> 4 a z - 3 a z - 8 z - ---- - 5 a z - 3 a z - ---- - 6 a z -
2 a
a
3 9 10 2 10
> 2 a z - z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 8 1 1 1 5 2 5 4 8
9 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
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
5 8 8 2 2 2 4 2 4 3
> ----- + ---- + ---- + 7 t + 7 q t + 4 q t + 7 q t + 3 q t +
4 2 4 2
q t q t q t
6 3 6 4 8 4 10 5
> 4 q t + q t + 3 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a60 |
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