 L10a143 |
 L10a145 |
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 Knotscape |
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The 3-Component Link L10a144Visit L10a144's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X14,4,15,3 X8,18,9,17 X16,8,17,7 X18,10,19,9 X10,14,11,13 X20,12,13,11 X12,20,5,19 X2536 X4,16,1,15 |
| Gauss Code: | {{1, -9, 2, -10}, {9, -1, 4, -3, 5, -6, 7, -8}, {6, -2, 10, -4, 3, -5, 8, -7}} |
| Jones Polynomial: | 1 - 2q + 5q2 - 6q3 + 8q4 - 8q5 + 9q6 - 6q7 + 4q8 - 2q9 + q10 |
| A2 (sl(3)) Invariant: | 1 + q4 + 2q6 + 3q10 + 3q14 + 4q16 + 3q18 + 5q20 + q22 + 2q24 + q26 + q30 |
| HOMFLY-PT Polynomial: | a-8z-2 + 2a-8 + 3a-8z2 + a-8z4 - 2a-6z-2 - 5a-6 - 6a-6z2 - 4a-6z4 - a-6z6 + a-4z-2 + a-4 - a-4z2 - 3a-4z4 - a-4z6 + 2a-2 + 3a-2z2 + a-2z4 |
| Kauffman Polynomial: | - 2a-12z2 + a-12z4 - 3a-11z3 + 2a-11z5 - 2a-10 + 6a-10z2 - 6a-10z4 + 3a-10z6 + a-9z + 4a-9z3 - 5a-9z5 + 3a-9z7 - a-8z-2 + 3a-8 - 5a-8z2 + 12a-8z4 - 8a-8z6 + 3a-8z8 + 2a-7z-1 - 8a-7z + 14a-7z3 - 10a-7z5 + 2a-7z7 + a-7z9 - 2a-6z-2 + 9a-6 - 19a-6z2 + 22a-6z4 - 16a-6z6 + 5a-6z8 + 2a-5z-1 - 8a-5z + 10a-5z3 - 9a-5z5 + a-5z7 + a-5z9 - a-4z-2 + 3a-4 - a-4z2 - a-4z4 - 4a-4z6 + 2a-4z8 + a-3z + 3a-3z3 - 6a-3z5 + 2a-3z7 - 2a-2 + 5a-2z2 - 4a-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, 144]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 144]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 4, 15, 3], X[8, 18, 9, 17], X[16, 8, 17, 7], > X[18, 10, 19, 9], X[10, 14, 11, 13], X[20, 12, 13, 11], X[12, 20, 5, 19], > X[2, 5, 3, 6], X[4, 16, 1, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 4, -3, 5, -6, 7, -8},
> {6, -2, 10, -4, 3, -5, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | 2 3 4 5 6 7 8 9 10 1 - 2 q + 5 q - 6 q + 8 q - 8 q + 9 q - 6 q + 4 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 4 6 10 14 16 18 20 22 24 26 30 1 + q + 2 q + 3 q + 3 q + 4 q + 3 q + 5 q + q + 2 q + q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 144]][a, z] |
Out[8]= | 2 2 2 2 4
2 5 -4 2 1 2 1 3 z 6 z z 3 z z
-- - -- + a + -- + ----- - ----- + ----- + ---- - ---- - -- + ---- + -- -
8 6 2 8 2 6 2 4 2 8 6 4 2 8
a a a a z a z a z a a a a a
4 4 4 6 6
4 z 3 z z z z
> ---- - ---- + -- - -- - --
6 4 2 6 4
a a a a a |
In[9]:= | Kauffman[Link[10, Alternating, 144]][a, z] |
Out[9]= | -2 3 9 3 2 1 2 1 2 2 z 8 z
--- + -- + -- + -- - -- - ----- - ----- - ----- + ---- + ---- + -- - --- -
10 8 6 4 2 8 2 6 2 4 2 7 5 9 7
a a a a a a z a z a z a z a z a a
2 2 2 2 2 2 3 3 3
8 z z 2 z 6 z 5 z 19 z z 5 z 3 z 4 z 14 z
> --- + -- - ---- + ---- - ---- - ----- - -- + ---- - ---- + ---- + ----- +
5 3 12 10 8 6 4 2 11 9 7
a a a a a a a a a a a
3 3 4 4 4 4 4 4 5 5
10 z 3 z z 6 z 12 z 22 z z 4 z 2 z 5 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 6 7 7 7
10 z 9 z 6 z 3 z 8 z 16 z 4 z z 3 z 2 z z
> ----- - ---- - ---- + ---- - ---- - ----- - ---- + -- + ---- + ---- + -- +
7 5 3 10 8 6 4 2 9 7 5
a a a a a a a a a a a
7 8 8 8 9 9
2 z 3 z 5 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
4 q + 3 q + ---- + - + -- + 4 q t + 2 q t + 4 q t + 4 q t + 4 q t +
2 t t
q t
11 3 11 4 13 4 13 5 15 5 15 6
> 4 q t + 5 q t + 5 q t + 2 q t + 4 q t + 2 q t +
17 6 19 7 19 8 21 8
> 2 q t + 2 q t + q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L10a144 |
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