 L10a149 |
 L10a151 |
| © | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: |
|
 Knotscape |
This page is passe. Go here
instead!
The 3-Component Link L10a150Visit L10a150's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X10,4,11,3 X12,8,13,7 X18,14,19,13 X16,10,17,9 X8,16,9,15 X20,18,15,17 X14,20,5,19 X2536 X4,12,1,11 |
| Gauss Code: | {{1, -9, 2, -10}, {6, -5, 7, -4, 8, -7}, {9, -1, 3, -6, 5, -2, 10, -3, 4, -8}} |
| Jones Polynomial: | 1 - 2q + 6q2 - 8q3 + 13q4 - 13q5 + 13q6 - 11q7 + 8q8 - 4q9 + q10 |
| A2 (sl(3)) Invariant: | 1 + 2q4 + 4q6 + q8 + 7q10 + 3q12 + 4q14 + 4q16 - q18 + 3q20 - 2q22 + q24 + q26 - 2q28 + q30 |
| HOMFLY-PT Polynomial: | a-8z2 + a-8z4 + a-6z-2 + a-6 - 2a-6z4 - a-6z6 - 2a-4z-2 - 4a-4 - 4a-4z2 - 3a-4z4 - a-4z6 + a-2z-2 + 3a-2 + 3a-2z2 + a-2z4 |
| Kauffman Polynomial: | a-12z4 - 2a-11z3 + 4a-11z5 - a-10 + 3a-10z2 - 9a-10z4 + 8a-10z6 - a-9z + 5a-9z3 - 12a-9z5 + 9a-9z7 - 3a-8 + 11a-8z2 - 15a-8z4 + 2a-8z6 + 5a-8z8 - 3a-7z + 16a-7z3 - 29a-7z5 + 13a-7z7 + a-7z9 + a-6z-2 - 7a-6 + 18a-6z2 - 13a-6z4 - 7a-6z6 + 7a-6z8 - 2a-5z-1 + a-5z + 11a-5z3 - 18a-5z5 + 6a-5z7 + a-5z9 + 2a-4z-2 - 8a-4 + 16a-4z2 - 12a-4z4 + 2a-4z8 - 2a-3z-1 + 3a-3z + 2a-3z3 - 5a-3z5 + 2a-3z7 + a-2z-2 - 4a-2 + 6a-2z2 - 4a-2z4 + a-2z6 |
| 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[10, Alternating, 150]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 150]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 4, 11, 3], X[12, 8, 13, 7], X[18, 14, 19, 13], > X[16, 10, 17, 9], X[8, 16, 9, 15], X[20, 18, 15, 17], X[14, 20, 5, 19], > X[2, 5, 3, 6], X[4, 12, 1, 11]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {6, -5, 7, -4, 8, -7},
> {9, -1, 3, -6, 5, -2, 10, -3, 4, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | 2 3 4 5 6 7 8 9 10 1 - 2 q + 6 q - 8 q + 13 q - 13 q + 13 q - 11 q + 8 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 4 6 8 10 12 14 16 18 20 22
1 + 2 q + 4 q + q + 7 q + 3 q + 4 q + 4 q - q + 3 q - 2 q +
24 26 28 30
> q + q - 2 q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 150]][a, z] |
Out[8]= | 2 2 2 4 4 4
-6 4 3 1 2 1 z 4 z 3 z z 2 z 3 z
a - -- + -- + ----- - ----- + ----- + -- - ---- + ---- + -- - ---- - ---- +
4 2 6 2 4 2 2 2 8 4 2 8 6 4
a a a z a z a z a a a a a a
4 6 6
z z z
> -- - -- - --
2 6 4
a a a |
In[9]:= | Kauffman[Link[10, Alternating, 150]][a, z] |
Out[9]= | -10 3 7 8 4 1 2 1 2 2 z 3 z
-a - -- - -- - -- - -- + ----- + ----- + ----- - ---- - ---- - -- - --- +
8 6 4 2 6 2 4 2 2 2 5 3 9 7
a a a a a z a z a z a z a z a a
2 2 2 2 2 3 3 3
z 3 z 3 z 11 z 18 z 16 z 6 z 2 z 5 z 16 z
> -- + --- + ---- + ----- + ----- + ----- + ---- - ---- + ---- + ----- +
5 3 10 8 6 4 2 11 9 7
a a a a a a a a a a
3 3 4 4 4 4 4 4 5 5
11 z 2 z z 9 z 15 z 13 z 12 z 4 z 4 z 12 z
> ----- + ---- + --- - ---- - ----- - ----- - ----- - ---- + ---- - ----- -
5 3 12 10 8 6 4 2 11 9
a a a a a a a a a a
5 5 5 6 6 6 6 7 7 7
29 z 18 z 5 z 8 z 2 z 7 z z 9 z 13 z 6 z
> ----- - ----- - ---- + ---- + ---- - ---- + -- + ---- + ----- + ---- +
7 5 3 10 8 6 2 9 7 5
a a a a a a a a a a
7 8 8 8 9 9
2 z 5 z 7 z 2 z z z
> ---- + ---- + ---- + ---- + -- + --
3 8 6 4 7 5
a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3
3 5 1 q q 5 7 7 2 9 2 9 3
5 q + 3 q + ---- + - + -- + 5 q t + 3 q t + 8 q t + 5 q t + 5 q t +
2 t t
q t
11 3 11 4 13 4 13 5 15 5 15 6
> 8 q t + 8 q t + 7 q t + 5 q t + 6 q t + 3 q t +
17 6 17 7 19 7 21 8
> 5 q t + q t + 3 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L10a150 |
|