 L10a144 |
 L10a146 |
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The 3-Component Link L10a145Visit L10a145's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X6172 X14,4,15,3 X8,18,9,17 X16,8,17,7 X18,10,19,9 X20,12,13,11 X12,14,5,13 X10,20,11,19 X2536 X4,16,1,15 |
| Gauss Code: | {{1, -9, 2, -10}, {9, -1, 4, -3, 5, -8, 6, -7}, {7, -2, 10, -4, 3, -5, 8, -6}} |
| Jones Polynomial: | q - q2 + 3q3 - 2q4 + 4q5 - 4q6 + 4q7 - 3q8 + 3q9 - 2q10 + q11 |
| A2 (sl(3)) Invariant: | q4 + q6 + 2q8 + 3q10 + 3q12 + 4q14 + 2q16 + 3q18 + q20 + 2q22 + 2q24 + q26 + q28 + q32 |
| HOMFLY-PT Polynomial: | a-8z-2 + 4a-8 + 7a-8z2 + 5a-8z4 + a-8z6 - 2a-6z-2 - 11a-6 - 19a-6z2 - 17a-6z4 - 7a-6z6 - a-6z8 + a-4z-2 + 7a-4 + 11a-4z2 + 6a-4z4 + a-4z6 |
| Kauffman Polynomial: | a-14z2 + 2a-13z3 + a-12 - 3a-12z2 + 3a-12z4 - 4a-11z3 + 3a-11z5 - 6a-10z4 + 3a-10z6 + 4a-9z3 - 9a-9z5 + 3a-9z7 - a-8z-2 + 5a-8 - 13a-8z2 + 20a-8z4 - 14a-8z6 + 3a-8z8 + 2a-7z-1 - 11a-7z + 19a-7z3 - 8a-7z5 - 2a-7z7 + a-7z9 - 2a-6z-2 + 13a-6 - 35a-6z2 + 46a-6z4 - 24a-6z6 + 4a-6z8 + 2a-5z-1 - 11a-5z + 9a-5z3 + 4a-5z5 - 5a-5z7 + a-5z9 - a-4z-2 + 8a-4 - 18a-4z2 + 17a-4z4 - 7a-4z6 + a-4z8 |
| 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, 145]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 145]] |
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[20, 12, 13, 11], X[12, 14, 5, 13], X[10, 20, 11, 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, -8, 6, -7},
> {7, -2, 10, -4, 3, -5, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | 2 3 4 5 6 7 8 9 10 11 q - q + 3 q - 2 q + 4 q - 4 q + 4 q - 3 q + 3 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 4 6 8 10 12 14 16 18 20 22 24
q + q + 2 q + 3 q + 3 q + 4 q + 2 q + 3 q + q + 2 q + 2 q +
26 28 32
> q + q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 145]][a, z] |
Out[8]= | 2 2 2 4 4
4 11 7 1 2 1 7 z 19 z 11 z 5 z 17 z
-- - -- + -- + ----- - ----- + ----- + ---- - ----- + ----- + ---- - ----- +
8 6 4 8 2 6 2 4 2 8 6 4 8 6
a a a a z a z a z a a a a a
4 6 6 6 8
6 z z 7 z z z
> ---- + -- - ---- + -- - --
4 8 6 4 6
a a a a a |
In[9]:= | Kauffman[Link[10, Alternating, 145]][a, z] |
Out[9]= | 2
-12 5 13 8 1 2 1 2 2 11 z 11 z z
a + -- + -- + -- - ----- - ----- - ----- + ---- + ---- - ---- - ---- + --- -
8 6 4 8 2 6 2 4 2 7 5 7 5 14
a a a a z a z a z a z a z a a a
2 2 2 2 3 3 3 3 3 4
3 z 13 z 35 z 18 z 2 z 4 z 4 z 19 z 9 z 3 z
> ---- - ----- - ----- - ----- + ---- - ---- + ---- + ----- + ---- + ---- -
12 8 6 4 13 11 9 7 5 12
a a a a a a a a a a
4 4 4 4 5 5 5 5 6 6
6 z 20 z 46 z 17 z 3 z 9 z 8 z 4 z 3 z 14 z
> ---- + ----- + ----- + ----- + ---- - ---- - ---- + ---- + ---- - ----- -
10 8 6 4 11 9 7 5 10 8
a a a a a a a a a a
6 6 7 7 7 8 8 8 9 9
24 z 7 z 3 z 2 z 5 z 3 z 4 z z z z
> ----- - ---- + ---- - ---- - ---- + ---- + ---- + -- + -- + --
6 4 9 7 5 8 6 4 7 5
a a a a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5
5 7 q q 7 9 9 2 11 2 11 3 13 3
3 q + 2 q + -- + -- + q t + q t + 3 q t + q t + q t + 3 q t +
2 t
t
13 4 15 4 15 5 17 5 17 6 19 6 21 7
> 3 q t + 2 q t + q t + 2 q t + 2 q t + q t + 2 q t +
21 8 23 8
> q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L10a145 |
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