 L11n265 |
 L11n267 |
| © | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: |
|
 Knotscape |
This page is passe. Go here
instead!
The 3-Component Link L11n266Visit L11n266's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X3,11,4,10 X7,15,8,14 X13,5,14,8 X18,11,19,12 X20,15,21,16 X22,17,9,18 X16,21,17,22 X12,19,13,20 X2536 X9,1,10,4 |
| Gauss Code: | {{1, -10, -2, 11}, {10, -1, -3, 4}, {-11, 2, 5, -9, -4, 3, 6, -8, 7, -5, 9, -6, 8, -7}} |
| Jones Polynomial: | - q-8 + 2q-7 - 5q-6 + 5q-5 - 5q-4 + 6q-3 - 3q-2 + 3q-1 + 1 + q2 |
| A2 (sl(3)) Invariant: | - q-24 - 4q-20 - 4q-18 - 3q-16 - 4q-14 + q-12 + q-10 + 6q-8 + 7q-6 + 7q-4 + 9q-2 + 5 + 4q2 + 2q4 + q6 |
| HOMFLY-PT Polynomial: | 3z-2 + 7 + 5z2 + z4 - 8a2z-2 - 20a2 - 19a2z2 - 8a2z4 - a2z6 + 7a4z-2 + 18a4 + 16a4z2 + 6a4z4 + a4z6 - 2a6z-2 - 5a6 - 3a6z2 - a6z4 |
| Kauffman Polynomial: | - 3z-2 + 13 - 24z2 + 21z4 - 8z6 + z8 + 8az-1 - 24az + 26az3 - 10az5 + az7 - 8a2z-2 + 28a2 - 45a2z2 + 36a2z4 - 11a2z6 + a2z8 + 15a3z-1 - 45a3z + 47a3z3 - 16a3z5 + 2a3z7 - 7a4z-2 + 22a4 - 27a4z2 + 18a4z4 - 5a4z6 + a4z8 + 7a5z-1 - 21a5z + 19a5z3 - 9a5z5 + 3a5z7 - 2a6z-2 + 7a6 - 6a6z2 - a6z4 + a6z8 - a7z-1 + 3a7z - 5a7z3 - 2a7z5 + 2a7z7 + a8 - 4a8z4 + 2a8z6 - a9z-1 + 3a9z - 3a9z3 + a9z5 |
| 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]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, NonAlternating, 266]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 266]] |
Out[4]= | PD[X[6, 1, 7, 2], X[3, 11, 4, 10], X[7, 15, 8, 14], X[13, 5, 14, 8], > X[18, 11, 19, 12], X[20, 15, 21, 16], X[22, 17, 9, 18], X[16, 21, 17, 22], > X[12, 19, 13, 20], X[2, 5, 3, 6], X[9, 1, 10, 4]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, -2, 11}, {10, -1, -3, 4},
> {-11, 2, 5, -9, -4, 3, 6, -8, 7, -5, 9, -6, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -8 2 5 5 5 6 3 3 2
1 - q + -- - -- + -- - -- + -- - -- + - + q
7 6 5 4 3 2 q
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 4 4 3 4 -12 -10 6 7 7 9 2
5 - q - --- - --- - --- - --- + q + q + -- + -- + -- + -- + 4 q +
20 18 16 14 8 6 4 2
q q q q q q q q
4 6
> 2 q + q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 266]][a, z] |
Out[8]= | 2 4 6
2 4 6 3 8 a 7 a 2 a 2 2 2
7 - 20 a + 18 a - 5 a + -- - ---- + ---- - ---- + 5 z - 19 a z +
2 2 2 2
z z z z
4 2 6 2 4 2 4 4 4 6 4 2 6 4 6
> 16 a z - 3 a z + z - 8 a z + 6 a z - a z - a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 266]][a, z] |
Out[9]= | 2 4 6 3 5
2 4 6 8 3 8 a 7 a 2 a 8 a 15 a 7 a
13 + 28 a + 22 a + 7 a + a - -- - ---- - ---- - ---- + --- + ----- + ---- -
2 2 2 2 z z z
z z z z
7 9
a a 3 5 7 9 2 2 2
> -- - -- - 24 a z - 45 a z - 21 a z + 3 a z + 3 a z - 24 z - 45 a z -
z z
4 2 6 2 3 3 3 5 3 7 3 9 3
> 27 a z - 6 a z + 26 a z + 47 a z + 19 a z - 5 a z - 3 a z +
4 2 4 4 4 6 4 8 4 5 3 5
> 21 z + 36 a z + 18 a z - a z - 4 a z - 10 a z - 16 a z -
5 5 7 5 9 5 6 2 6 4 6 8 6 7
> 9 a z - 2 a z + a z - 8 z - 11 a z - 5 a z + 2 a z + a z +
3 7 5 7 7 7 8 2 8 4 8 6 8
> 2 a z + 3 a z + 2 a z + z + a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 4 1 1 1 4 1 1 4 4
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
3 q 17 7 15 6 13 6 13 5 11 5 11 4 9 4 9 3
q q t q t q t q t q t q t q t q t
1 3 4 1 1 3 t 2 3 4 5 4
> ----- + ----- + ----- + ---- + ---- + ---- + -- + q t + q t + q t
7 3 7 2 5 2 7 5 3 3
q t q t q t q t q t q t q |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11n266 |
|