 L2a1 |
 L5a1 |
| © | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: |
|
 Knotscape |
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The 2-Component Link L4a1Visit L4a1's page at Knotilus! |
 DrawMorseLink |
| Further views: |
 Hearst Castle tile |
 Mosaic seen at Kibbutz Lahav |
| PD Presentation: | X6172 X8354 X2536 X4718 |
| Gauss Code: | {{1, -3, 2, -4}, {3, -1, 4, -2}} |
| Jones Polynomial: | - q-9/2 - q-5/2 + q-3/2 - q-1/2 |
| A2 (sl(3)) Invariant: | q-16 + 2q-14 + 2q-12 + 2q-10 + q-8 + 1 |
| HOMFLY-PT Polynomial: | - az - a3z-1 - a3z + a5z-1 |
| Kauffman Polynomial: | - az - a2z2 - a3z-1 + 2a3z - a3z3 + a4 - a4z2 - a5z-1 + 3a5z - a5z3 |
| 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[4, Alternating, 1]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[4, Alternating, 1]] |
Out[4]= | PD[X[6, 1, 7, 2], X[8, 3, 5, 4], X[2, 5, 3, 6], X[4, 7, 1, 8]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -3, 2, -4}, {3, -1, 4, -2}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(9/2) -(5/2) -(3/2) 1
-q - q + q - -------
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -16 2 2 2 -8
1 + q + --- + --- + --- + q
14 12 10
q q q |
In[8]:= | HOMFLYPT[Link[4, Alternating, 1]][a, z] |
Out[8]= | 3 5 a a 3 -(--) + -- - a z - a z z z |
In[9]:= | Kauffman[Link[4, Alternating, 1]][a, z] |
Out[9]= | 3 5
4 a a 3 5 2 2 4 2 3 3 5 3
a - -- - -- - a z + 2 a z + 3 a z - a z - a z - a z - a z
z z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -2 1 1 1 1
1 + q + ------ + ----- + ----- + ----
10 4 8 4 6 2 2
q t q t q t q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L4a1 |
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