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Acknowledgement

L11a64 as Morse Link
DrawMorseLink

PD Presentation: X6172 X12,4,13,3 X14,8,15,7 X18,10,19,9 X22,16,5,15 X16,22,17,21 X20,12,21,11 X8,18,9,17 X10,20,11,19 X2536 X4,14,1,13

Gauss Code: {{1, -10, 2, -11}, {10, -1, 3, -8, 4, -9, 7, -2, 11, -3, 5, -6, 8, -4, 9, -7, 6, -5}}

Jones Polynomial: - q1/2 + 2q3/2 - 5q5/2 + 7q7/2 - 12q9/2 + 13q11/2 - 14q13/2 + 13q15/2 - 10q17/2 + 7q19/2 - 3q21/2 + q23/2

A2 (sl(3)) Invariant: q2 + q6 + 2q8 + 5q12 + q14 + 4q16 + 3q18 - q20 + 2q22 - 4q24 - q26 - 2q28 - 2q30 + q32 - q34

HOMFLY-PT Polynomial: 2a-9z-1 + 3a-9z + 3a-9z3 + a-9z5 - 4a-7z-1 - 7a-7z - 6a-7z3 - 4a-7z5 - a-7z7 + a-5z-1 - 4a-5z3 - 4a-5z5 - a-5z7 + a-3z-1 + 4a-3z + 4a-3z3 + a-3z5

Kauffman Polynomial: a-14z2 - a-14z4 + 2a-13z3 - 3a-13z5 + 2a-12 - 6a-12z2 + 8a-12z4 - 6a-12z6 - a-11z - 4a-11z3 + 9a-11z5 - 7a-11z7 + a-10 - 4a-10z2 + 7a-10z6 - 6a-10z8 + 2a-9z-1 - 8a-9z + 15a-9z3 - 9a-9z5 + 6a-9z7 - 4a-9z9 - 6a-8 + 19a-8z2 - 24a-8z4 + 21a-8z6 - 6a-8z8 - a-8z10 + 4a-7z-1 - 13a-7z + 24a-7z3 - 25a-7z5 + 19a-7z7 - 6a-7z9 - 5a-6 + 16a-6z2 - 23a-6z4 + 16a-6z6 - 2a-6z8 - a-6z10 + a-5z-1 - a-5z - 5a-5z3 + a-5z5 + 5a-5z7 - 2a-5z9 + a-4 - 8a-4z4 + 8a-4z6 - 2a-4z8 - a-3z-1 + 5a-3z - 8a-3z3 + 5a-3z5 - a-3z7

Khovanov Homology:
trqj r = -2r = -1r = 0r = 1r = 2r = 3r = 4r = 5r = 6r = 7r = 8r = 9
j = 24           1
j = 22          2 
j = 20         51 
j = 18        52  
j = 16       85   
j = 14      65    
j = 12     78     
j = 10    56      
j = 8   27       
j = 6  35        
j = 4 14         
j = 2 1          
j = 01           


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]=   
2
In[3]:=
Show[DrawMorseLink[Link[11, Alternating, 64]]]
Out[3]=   
 -Graphics- 
In[4]:=
PD[L = Link[11, Alternating, 64]]
Out[4]=   
PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[14, 8, 15, 7], X[18, 10, 19, 9], 
 
>   X[22, 16, 5, 15], X[16, 22, 17, 21], X[20, 12, 21, 11], X[8, 18, 9, 17], 
 
>   X[10, 20, 11, 19], X[2, 5, 3, 6], X[4, 14, 1, 13]]
In[5]:=
GaussCode[L]
Out[5]=   
GaussCode[{1, -10, 2, -11}, {10, -1, 3, -8, 4, -9, 7, -2, 11, -3, 5, -6, 8, -4, 
 
>    9, -7, 6, -5}]
In[6]:=
Jones[L][q]
Out[6]=   
              3/2      5/2      7/2       9/2       11/2       13/2
-Sqrt[q] + 2 q    - 5 q    + 7 q    - 12 q    + 13 q     - 14 q     + 
 
        15/2       17/2      19/2      21/2    23/2
>   13 q     - 10 q     + 7 q     - 3 q     + q
In[7]:=
A2Invariant[L][q]
Out[7]=   
 2    6      8      12    14      16      18    20      22      24    26
q  + q  + 2 q  + 5 q   + q   + 4 q   + 3 q   - q   + 2 q   - 4 q   - q   - 
 
       28      30    32    34
>   2 q   - 2 q   + q   - q
In[8]:=
HOMFLYPT[Link[11, Alternating, 64]][a, z]
Out[8]=   
                                                 3      3      3      3    5
 2      4      1      1     3 z   7 z   4 z   3 z    6 z    4 z    4 z    z
---- - ---- + ---- + ---- + --- - --- + --- + ---- - ---- - ---- + ---- + -- - 
 9      7      5      3      9     7     3      9      7      5      3     9
a  z   a  z   a  z   a  z   a     a     a      a      a      a      a     a
 
       5      5    5    7    7
    4 z    4 z    z    z    z
>   ---- - ---- + -- - -- - --
      7      5     3    7    5
     a      a     a    a    a
In[9]:=
Kauffman[Link[11, Alternating, 64]][a, z]
Out[9]=   
 2     -10   6    5     -4    2      4      1      1      z    8 z   13 z
--- + a    - -- - -- + a   + ---- + ---- + ---- - ---- - --- - --- - ---- - 
 12           8    6          9      7      5      3      11    9      7
a            a    a          a  z   a  z   a  z   a  z   a     a      a
 
                2       2      2       2       2      3      3       3
    z    5 z   z     6 z    4 z    19 z    16 z    2 z    4 z    15 z
>   -- + --- + --- - ---- - ---- + ----- + ----- + ---- - ---- + ----- + 
     5    3     14    12     10      8       6      13     11      9
    a    a     a     a      a       a       a      a      a       a
 
        3      3      3    4       4       4       4      4      5      5
    24 z    5 z    8 z    z     8 z    24 z    23 z    8 z    3 z    9 z
>   ----- - ---- - ---- - --- + ---- - ----- - ----- - ---- - ---- + ---- - 
      7       5      3     14    12      8       6       4     13     11
     a       a      a     a     a       a       a       a     a      a
 
       5       5    5      5      6      6       6       6      6      7
    9 z    25 z    z    5 z    6 z    7 z    21 z    16 z    8 z    7 z
>   ---- - ----- + -- + ---- - ---- + ---- + ----- + ----- + ---- - ---- + 
      9      7      5     3     12     10      8       6       4     11
     a      a      a     a     a      a       a       a       a     a
 
       7       7      7    7      8      8      8      8      9      9      9
    6 z    19 z    5 z    z    6 z    6 z    2 z    2 z    4 z    6 z    2 z
>   ---- + ----- + ---- - -- - ---- - ---- - ---- - ---- - ---- - ---- - ---- - 
      9      7       5     3    10      8      6      4      9      7      5
     a      a       a     a    a       a      a      a      a      a      a
 
     10    10
    z     z
>   --- - ---
     8     6
    a     a
In[10]:=
Kh[L][q, t]
Out[10]=   
                     2    4
   4      6    -2   q    q       6        8        8  2      10  2      10  3
4 q  + 3 q  + t   + -- + -- + 5 q  t + 2 q  t + 7 q  t  + 5 q   t  + 6 q   t  + 
                    t    t
 
       12  3      12  4      14  4      14  5      16  5      16  6
>   7 q   t  + 8 q   t  + 6 q   t  + 5 q   t  + 8 q   t  + 5 q   t  + 
 
       18  6      18  7      20  7    20  8      22  8    24  9
>   5 q   t  + 2 q   t  + 5 q   t  + q   t  + 2 q   t  + q   t


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