PD Presentation: |
X6172 X12,4,13,3 X16,8,17,7 X20,12,21,11 X22,18,5,17 X18,22,19,21 X10,20,11,19 X14,10,15,9 X8,16,9,15 X2536 X4,14,1,13 |
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, 68]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 68]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[16, 8, 17, 7], X[20, 12, 21, 11],
> X[22, 18, 5, 17], X[18, 22, 19, 21], X[10, 20, 11, 19], X[14, 10, 15, 9],
> X[8, 16, 9, 15], X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -9, 8, -7, 4, -2, 11, -8, 9, -3, 5, -6,
> 7, -4, 6, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | 1 3/2 5/2 7/2 9/2 11/2
-(-------) + 2 Sqrt[q] - 6 q + 10 q - 15 q + 16 q - 17 q +
Sqrt[q]
13/2 15/2 17/2 19/2 21/2
> 15 q - 11 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -2 2 4 6 8 10 12 14 16 18 22
q + q + 4 q - 2 q + 3 q + 2 q - q + 4 q - q + 3 q - 2 q +
24 26 28 30 32
> 2 q - 4 q - q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 68]][a, z] |
Out[8]= | 3 3 3 3
1 2 1 1 1 z 2 z z 2 z z z 3 z z
---- - ---- + ---- - ---- + --- + -- - --- - -- + --- + -- - -- - ---- - -- +
9 7 5 3 a z 9 7 3 a 9 7 5 3
a z a z a z a z a a a a a a a
3 5 5 5
z z 2 z z
> -- - -- - ---- - --
a 7 5 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 68]][a, z] |
Out[9]= | -3 7 4 -2 1 2 1 1 1 3 z 6 z 3 z 3 z
--- - -- - -- - a + ---- + ---- + ---- + ---- + --- - --- - --- - --- - --- -
10 8 6 9 7 5 3 a z 9 7 5 3
a a a a z a z a z a z a a a a
2 2 2 2 2 3 3 3 3
3 z 2 z 9 z 26 z 17 z 2 z 5 z 6 z 10 z z
> --- - ---- + ---- + ----- + ----- + ---- - ---- + ---- + ----- - -- +
a 12 10 8 6 4 11 9 7 5
a a a a a a a a a
3 3 4 4 4 4 4 4 5 5
3 z 3 z 3 z 14 z 37 z 28 z 5 z 3 z 8 z 4 z
> ---- + ---- + ---- - ----- - ----- - ----- - ---- + ---- + ---- - ---- -
3 a 12 10 8 6 4 2 11 9
a a a a a a a a a
5 5 5 5 6 6 6 6 6 6
12 z 3 z 2 z z z 14 z 30 z 22 z 5 z 2 z
> ----- + ---- + ---- - -- - --- + ----- + ----- + ----- + ---- - ---- -
7 5 3 a 12 10 8 6 4 2
a a a a a a a a a
7 7 7 7 8 8 8 8 9 9
3 z 7 z 13 z 3 z 5 z 9 z 8 z 4 z 4 z 7 z
> ---- + ---- + ----- - ---- - ---- - ---- - ---- - ---- - ---- - ---- -
11 9 7 3 10 8 6 4 9 7
a a a a a a a a a a
9 10 10
3 z z z
> ---- - --- - ---
5 8 6
a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 1 q 4 6 6 2 8 2 8 3
5 q + 3 q + ----- + - + -- + 7 q t + 3 q t + 8 q t + 7 q t + 8 q t +
2 2 t t
q t
10 3 10 4 12 4 12 5 14 5 14 6
> 8 q t + 9 q t + 8 q t + 6 q t + 9 q t + 5 q t +
16 6 16 7 18 7 18 8 20 8 22 9
> 6 q t + 2 q t + 5 q t + q t + 2 q t + q t |