 L11a109 |
 L11a111 |
| © | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: |
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 Knotscape |
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The 2-Component Link L11a110Visit L11a110's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X14,4,15,3 X16,8,17,7 X18,10,19,9 X20,12,21,11 X22,14,5,13 X8,18,9,17 X10,20,11,19 X12,22,13,21 X2536 X4,16,1,15 |
| Gauss Code: | {{1, -10, 2, -11}, {10, -1, 3, -7, 4, -8, 5, -9, 6, -2, 11, -3, 7, -4, 8, -5, 9, -6}} |
| Jones Polynomial: | - q3/2 + q5/2 - 3q7/2 + 2q9/2 - 4q11/2 + 4q13/2 - 4q15/2 + 4q17/2 - 3q19/2 + 3q21/2 - 2q23/2 + q25/2 |
| A2 (sl(3)) Invariant: | q6 + q8 + 2q10 + 3q12 + 3q14 + 4q16 + 2q18 + 2q20 - q22 - q24 - 2q26 - 2q28 - q30 - q32 - q36 |
| HOMFLY-PT Polynomial: | 3a-9z-1 + 8a-9z + 11a-9z3 + 6a-9z5 + a-9z7 - 7a-7z-1 - 22a-7z - 31a-7z3 - 23a-7z5 - 8a-7z7 - a-7z9 + 4a-5z-1 + 14a-5z + 16a-5z3 + 7a-5z5 + a-5z7 |
| Kauffman Polynomial: | - a-16z2 - 2a-15z3 - a-14 + 3a-14z2 - 3a-14z4 + 4a-13z3 - 3a-13z5 + 6a-12z4 - 3a-12z6 - 4a-11z3 + 9a-11z5 - 3a-11z7 - 10a-10z4 + 12a-10z6 - 3a-10z8 + 3a-9z-1 - 12a-9z + 25a-9z3 - 31a-9z5 + 17a-9z7 - 3a-9z9 - 7a-8 + 23a-8z2 - 27a-8z4 + 7a-8z6 + 3a-8z8 - a-8z10 + 7a-7z-1 - 30a-7z + 65a-7z3 - 66a-7z5 + 28a-7z7 - 4a-7z9 - 7a-6 + 19a-6z2 - 8a-6z4 - 8a-6z6 + 6a-6z8 - a-6z10 + 4a-5z-1 - 18a-5z + 30a-5z3 - 23a-5z5 + 8a-5z7 - a-5z9 |
| 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, 110]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 110]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 4, 15, 3], X[16, 8, 17, 7], X[18, 10, 19, 9], > X[20, 12, 21, 11], X[22, 14, 5, 13], X[8, 18, 9, 17], X[10, 20, 11, 19], > X[12, 22, 13, 21], X[2, 5, 3, 6], X[4, 16, 1, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -7, 4, -8, 5, -9, 6, -2, 11, -3, 7, -4,
> 8, -5, 9, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | 3/2 5/2 7/2 9/2 11/2 13/2 15/2 17/2
-q + q - 3 q + 2 q - 4 q + 4 q - 4 q + 4 q -
19/2 21/2 23/2 25/2
> 3 q + 3 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 6 8 10 12 14 16 18 20 22 24 26
q + q + 2 q + 3 q + 3 q + 4 q + 2 q + 2 q - q - q - 2 q -
28 30 32 36
> 2 q - q - q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 110]][a, z] |
Out[8]= | 3 3 3 5 5
3 7 4 8 z 22 z 14 z 11 z 31 z 16 z 6 z 23 z
---- - ---- + ---- + --- - ---- + ---- + ----- - ----- + ----- + ---- - ----- +
9 7 5 9 7 5 9 7 5 9 7
a z a z a z a a a a a a a a
5 7 7 7 9
7 z z 8 z z z
> ---- + -- - ---- + -- - --
5 9 7 5 7
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 110]][a, z] |
Out[9]= | 2 2
-14 7 7 3 7 4 12 z 30 z 18 z z 3 z
-a - -- - -- + ---- + ---- + ---- - ---- - ---- - ---- - --- + ---- +
8 6 9 7 5 9 7 5 16 14
a a a z a z a z a a a a a
2 2 3 3 3 3 3 3 4 4
23 z 19 z 2 z 4 z 4 z 25 z 65 z 30 z 3 z 6 z
> ----- + ----- - ---- + ---- - ---- + ----- + ----- + ----- - ---- + ---- -
8 6 15 13 11 9 7 5 14 12
a a a a a a a a a a
4 4 4 5 5 5 5 5 6 6
10 z 27 z 8 z 3 z 9 z 31 z 66 z 23 z 3 z 12 z
> ----- - ----- - ---- - ---- + ---- - ----- - ----- - ----- - ---- + ----- +
10 8 6 13 11 9 7 5 12 10
a a a a a a a a a a
6 6 7 7 7 7 8 8 8 9
7 z 8 z 3 z 17 z 28 z 8 z 3 z 3 z 6 z 3 z
> ---- - ---- - ---- + ----- + ----- + ---- - ---- + ---- + ---- - ---- -
8 6 11 9 7 5 10 8 6 9
a a a a a a a a a a
9 9 10 10
4 z z z z
> ---- - -- - --- - ---
7 5 8 6
a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 6
6 8 q q 8 10 10 2 12 2 12 3 14 3
3 q + 2 q + -- + -- + q t + q t + 3 q t + q t + q t + 3 q t +
2 t
t
14 4 16 4 16 5 18 5 18 6 20 6 20 7
> 3 q t + q t + q t + 3 q t + 2 q t + q t + q t +
22 7 22 8 24 8 26 9
> 2 q t + q t + q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a110 |
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