PD Presentation: |
X6172 X10,3,11,4 X16,12,17,11 X18,22,19,21 X20,14,21,13 X12,20,13,19 X22,18,9,17 X8,16,5,15 X14,8,15,7 X2536 X4,9,1,10 |
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[11, Alternating, 385]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 385]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[16, 12, 17, 11], X[18, 22, 19, 21],
> X[20, 14, 21, 13], X[12, 20, 13, 19], X[22, 18, 9, 17], X[8, 16, 5, 15],
> X[14, 8, 15, 7], X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 9, -8},
> {11, -2, 3, -6, 5, -9, 8, -3, 7, -4, 6, -5, 4, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -3 2 7 2 3 4 5 6 7 8
-10 + q - -- + - + 17 q - 19 q + 21 q - 18 q + 14 q - 10 q + 4 q - q
2 q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 -8 -6 6 3 2 4 6 8 12 14 16
5 + q + q + q + -- + -- + 10 q + 2 q + 7 q + q + q - 6 q + q -
4 2
q q
18 20 22 24
> 4 q - 3 q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 385]][a, z] |
Out[8]= | 2 2
2 6 3 2 -2 1 3 2 a 2 z
-3 - -- + -- - -- + 2 a - z - ----- + ----- - ----- + -- - 4 z - -- +
6 4 2 6 2 4 2 2 2 2 6
a a a a z a z a z z a
2 2 4 4 4 6 6
4 z z 2 2 4 z 2 z z z z
> ---- - -- + a z - 2 z - -- + ---- + -- + -- + --
4 2 6 4 2 4 2
a a a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 385]][a, z] |
Out[9]= | 2
-6 5 4 2 -2 1 3 2 a 2 8
-3 + a + -- + -- - 4 a + z - ----- - ----- - ----- + -- + ---- + ---- +
4 2 6 2 4 2 2 2 2 7 5
a a a z a z a z z a z a z
2 2
10 2 2 a 7 z 27 z 34 z 10 z 2 2 z 4 z
> ---- + --- - --- - --- - ---- - ---- - ---- + 4 a z + 5 z - ---- - ---- -
3 a z z 7 5 3 a 6 4
a z a a a a a
2 3 3 3 3 3 4 4
3 z 2 2 z 11 z 39 z 50 z 23 z 4 4 z 10 z
> ---- + 6 a z - -- + ----- + ----- + ----- + ----- - 2 z - ---- + ----- +
2 9 7 5 3 a 8 6
a a a a a a a
4 4 5 5 5 5 5
18 z 6 z 2 4 z 16 z 31 z 33 z 23 z 5
> ----- + ---- - 4 a z + -- - ----- - ----- - ----- - ----- - 4 a z -
4 2 9 7 5 3 a
a a a a a a
6 6 6 6 7 7 7 7
6 4 z 17 z 31 z 15 z 2 6 9 z 6 z z 6 z
> 4 z + ---- - ----- - ----- - ----- + a z + ---- + ---- + -- + ---- +
8 6 4 2 7 5 3 a
a a a a a a a
8 8 8 9 9 9 10 10
7 8 10 z 15 z 8 z 5 z 7 z 2 z z z
> 2 a z + 3 z + ----- + ----- + ---- + ---- + ---- + ---- + --- + ---
6 4 2 5 3 a 4 2
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 1 2 5 2 5 5 q 3
12 q + 8 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 10 q t +
7 4 5 4 5 3 3 2 2 q t t
q t q t q t q t q t
5 5 2 7 2 7 3 9 3 9 4 11 4
> 9 q t + 11 q t + 10 q t + 7 q t + 11 q t + 7 q t + 7 q t +
11 5 13 5 13 6 15 6 17 7
> 3 q t + 7 q t + q t + 3 q t + q t |