 L11a153 |
 L11a155 |
| © | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: |
|
 Knotscape |
This page is passe. Go here
instead!
The 2-Component Link L11a154Visit L11a154's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X8192 X10,3,11,4 X22,16,7,15 X14,5,15,6 X4,13,5,14 X20,18,21,17 X12,20,13,19 X18,12,19,11 X16,22,17,21 X2738 X6,9,1,10 |
| Gauss Code: | {{1, -10, 2, -5, 4, -11}, {10, -1, 11, -2, 8, -7, 5, -4, 3, -9, 6, -8, 7, -6, 9, -3}} |
| Jones Polynomial: | - q-13/2 + 2q-11/2 - 5q-9/2 + 8q-7/2 - 12q-5/2 + 13q-3/2 - 14q-1/2 + 12q1/2 - 9q3/2 + 6q5/2 - 3q7/2 + q9/2 |
| A2 (sl(3)) Invariant: | q-20 + q-16 + 3q-14 - q-12 + 3q-10 + 3q-8 + 3q-4 - 2q-2 + 1 - q2 - 2q4 + 2q6 - 2q8 + q12 - q14 |
| HOMFLY-PT Polynomial: | a-3z + a-3z3 + a-1z-1 + a-1z - a-1z3 - a-1z5 - 2az-1 - 5az - 5az3 - 2az5 - 2a3z - 2a3z3 - a3z5 + a5z-1 + 2a5z + a5z3 |
| Kauffman Polynomial: | - 2a-4z2 + 3a-4z4 - a-4z6 + a-3z - 6a-3z3 + 9a-3z5 - 3a-3z7 - 2a-2 + 5a-2z2 - 8a-2z4 + 11a-2z6 - 4a-2z8 + a-1z-1 - 2a-1z + a-1z5 + 5a-1z7 - 3a-1z9 - 5 + 23z2 - 34z4 + 23z6 - 5z8 - z10 + 2az-1 - 10az + 21az3 - 27az5 + 18az7 - 6az9 - 3a2 + 15a2z2 - 28a2z4 + 17a2z6 - 4a2z8 - a2z10 - a3z + 7a3z3 - 12a3z5 + 7a3z7 - 3a3z9 + a4 - 2a4z2 - a4z4 + 4a4z6 - 3a4z8 - a5z-1 + 4a5z - 5a5z3 + 6a5z5 - 3a5z7 - a6z2 + 4a6z4 - 2a6z6 - 2a7z + 3a7z3 - a7z5 |
| Khovanov Homology: |
|
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, 154]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 154]] |
Out[4]= | PD[X[8, 1, 9, 2], X[10, 3, 11, 4], X[22, 16, 7, 15], X[14, 5, 15, 6], > X[4, 13, 5, 14], X[20, 18, 21, 17], X[12, 20, 13, 19], X[18, 12, 19, 11], > X[16, 22, 17, 21], X[2, 7, 3, 8], X[6, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -5, 4, -11},
> {10, -1, 11, -2, 8, -7, 5, -4, 3, -9, 6, -8, 7, -6, 9, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 2 5 8 12 13 14 3/2
-q + ----- - ---- + ---- - ---- + ---- - ------- + 12 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
> 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -20 -16 3 -12 3 3 3 2 2 4 6 8
1 + q + q + --- - q + --- + -- + -- - -- - q - 2 q + 2 q - 2 q +
14 10 8 4 2
q q q q q
12 14
> q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 154]][a, z] |
Out[8]= | 5 3 3
1 2 a a z z 3 5 z z 3
--- - --- + -- + -- + - - 5 a z - 2 a z + 2 a z + -- - -- - 5 a z -
a z z z 3 a 3 a
a a
5
3 3 5 3 z 5 3 5
> 2 a z + a z - -- - 2 a z - a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 154]][a, z] |
Out[9]= | 5
2 2 4 1 2 a a z 2 z 3 5
-5 - -- - 3 a + a + --- + --- - -- + -- - --- - 10 a z - a z + 4 a z -
2 a z z z 3 a
a a
2 2 3
7 2 2 z 5 z 2 2 4 2 6 2 6 z
> 2 a z + 23 z - ---- + ---- + 15 a z - 2 a z - a z - ---- +
4 2 3
a a a
4 4
3 3 3 5 3 7 3 4 3 z 8 z 2 4
> 21 a z + 7 a z - 5 a z + 3 a z - 34 z + ---- - ---- - 28 a z -
4 2
a a
5 5
4 4 6 4 9 z z 5 3 5 5 5 7 5
> a z + 4 a z + ---- + -- - 27 a z - 12 a z + 6 a z - a z +
3 a
a
6 6 7 7
6 z 11 z 2 6 4 6 6 6 3 z 5 z 7
> 23 z - -- + ----- + 17 a z + 4 a z - 2 a z - ---- + ---- + 18 a z +
4 2 3 a
a a a
8 9
3 7 5 7 8 4 z 2 8 4 8 3 z 9
> 7 a z - 3 a z - 5 z - ---- - 4 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]= | 8 1 1 2 3 2 5 3 7
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 7 2 2 2 4 2 4 3
> ----- + ---- + ---- + 5 t + 7 q t + 4 q t + 5 q t + 2 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 + 2 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a154 |
|