 L10a132 |
 L10a134 |
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The 3-Component Link L10a133Visit L10a133's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X12,4,13,3 X14,12,15,11 X20,16,11,15 X8,18,9,17 X16,8,17,7 X18,10,19,9 X10,20,5,19 X2536 X4,14,1,13 |
| Gauss Code: | {{1, -9, 2, -10}, {9, -1, 6, -5, 7, -8}, {3, -2, 10, -3, 4, -6, 5, -7, 8, -4}} |
| Jones Polynomial: | 1 - q + 4q2 - 5q3 + 8q4 - 8q5 + 9q6 - 7q7 + 5q8 - 3q9 + q10 |
| A2 (sl(3)) Invariant: | 1 + q2 + 2q4 + 4q6 + 2q8 + 5q10 + 2q12 + 3q14 + 4q16 + q18 + 3q20 - q22 - q28 + q30 |
| HOMFLY-PT Polynomial: | 2a-8z2 + a-8z4 + a-6z-2 + 2a-6 - a-6z2 - 3a-6z4 - a-6z6 - 2a-4z-2 - 6a-4 - 6a-4z2 - 4a-4z4 - a-4z6 + a-2z-2 + 4a-2 + 4a-2z2 + a-2z4 |
| Kauffman Polynomial: | - a-12z2 + a-12z4 - 4a-11z3 + 3a-11z5 + a-10z2 - 5a-10z4 + 4a-10z6 + 4a-9z3 - 6a-9z5 + 4a-9z7 + a-8 - 5a-8z2 + 9a-8z4 - 6a-8z6 + 3a-8z8 + 2a-7z3 - 3a-7z5 + a-7z7 + a-7z9 + a-6z-2 - 3a-6 - 2a-6z2 + 11a-6z4 - 11a-6z6 + 4a-6z8 - 2a-5z-1 + 6a-5z - 9a-5z3 + 4a-5z5 - 2a-5z7 + a-5z9 + 2a-4z-2 - 8a-4 + 13a-4z2 - 9a-4z4 + a-4z8 - 2a-3z-1 + 6a-3z - 3a-3z3 - 2a-3z5 + a-3z7 + a-2z-2 - 5a-2 + 8a-2z2 - 5a-2z4 + a-2z6 |
| 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]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[10, Alternating, 133]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 133]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[14, 12, 15, 11], X[20, 16, 11, 15], > X[8, 18, 9, 17], X[16, 8, 17, 7], X[18, 10, 19, 9], X[10, 20, 5, 19], > X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 6, -5, 7, -8},
> {3, -2, 10, -3, 4, -6, 5, -7, 8, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | 2 3 4 5 6 7 8 9 10 1 - q + 4 q - 5 q + 8 q - 8 q + 9 q - 7 q + 5 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 2 4 6 8 10 12 14 16 18 20
1 + q + 2 q + 4 q + 2 q + 5 q + 2 q + 3 q + 4 q + q + 3 q -
22 28 30
> q - q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 133]][a, z] |
Out[8]= | 2 2 2 2 4 4
2 6 4 1 2 1 2 z z 6 z 4 z z 3 z
-- - -- + -- + ----- - ----- + ----- + ---- - -- - ---- + ---- + -- - ---- -
6 4 2 6 2 4 2 2 2 8 6 4 2 8 6
a a a a z a z a z a a a a a a
4 4 6 6
4 z z z z
> ---- + -- - -- - --
4 2 6 4
a a a a |
In[9]:= | Kauffman[Link[10, Alternating, 133]][a, z] |
Out[9]= | 2
-8 3 8 5 1 2 1 2 2 6 z 6 z z
a - -- - -- - -- + ----- + ----- + ----- - ---- - ---- + --- + --- - --- +
6 4 2 6 2 4 2 2 2 5 3 5 3 12
a a a a z a z a z a z a z a a a
2 2 2 2 2 3 3 3 3 3 4
z 5 z 2 z 13 z 8 z 4 z 4 z 2 z 9 z 3 z z
> --- - ---- - ---- + ----- + ---- - ---- + ---- + ---- - ---- - ---- + --- -
10 8 6 4 2 11 9 7 5 3 12
a a a a a a a a a a a
4 4 4 4 4 5 5 5 5 5
5 z 9 z 11 z 9 z 5 z 3 z 6 z 3 z 4 z 2 z
> ---- + ---- + ----- - ---- - ---- + ---- - ---- - ---- + ---- - ---- +
10 8 6 4 2 11 9 7 5 3
a a a a a a a a a a
6 6 6 6 7 7 7 7 8 8 8 9
4 z 6 z 11 z z 4 z z 2 z z 3 z 4 z z z
> ---- - ---- - ----- + -- + ---- + -- - ---- + -- + ---- + ---- + -- + -- +
10 8 6 2 9 7 5 3 8 6 4 7
a a a a a a a a a a a a
9
z
> --
5
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3
3 5 1 q 5 7 7 2 9 2 9 3
4 q + 2 q + ---- + -- + 3 q t + 2 q t + 5 q t + 4 q t + 4 q t +
2 t
q t
11 3 11 4 13 4 13 5 15 5 15 6
> 4 q t + 5 q t + 4 q t + 2 q t + 5 q t + 3 q t +
17 6 17 7 19 7 21 8
> 3 q t + q t + 2 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L10a133 |
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