View source for L11n442

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{{Link Page|
n = 11 |
t = n |
k = 442 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,-4,5:2,-1,-6,7:-5,4,-3,10,-8,11:-7,6,-11,3,-9,8,-10,9/goTop.html |
khovanov_table  = <table border=1>
<tr align=center>
<td width=14.2857%><table cellpadding=0 cellspacing=0>
  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
  <td width=7.14286%>-2</td    ><td width=7.14286%>-1</td    ><td width=7.14286%>0</td    ><td width=7.14286%>1</td    ><td width=7.14286%>2</td    ><td width=7.14286%>3</td    ><td width=7.14286%>4</td    ><td width=7.14286%>5</td    ><td width=7.14286%>6</td    ><td width=7.14286%>7</td    ><td width=14.2857%>&chi;</td></tr>
<tr align=center><td>16</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr>
<tr align=center><td>14</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr>
<tr align=center><td>12</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>10</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>2</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>0</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>-2</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
</table> |
computer_talk =
         <table>
         <tr valign=top>
         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
         </tr>
         <tr valign=top><td colspan=2>Loading KnotTheory` (version of August 28, 2005, 22:58:49)...</td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[11, NonAlternating, 442]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Length[Skeleton[Link[11, NonAlternating, 442]]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Link[11, NonAlternating, 442]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 1, 7, 2], X[2, 5, 3, 6], X[11, 19, 12, 18], X[3, 11, 4, 10], 
 
  X[9, 1, 10, 4], X[7, 17, 8, 16], X[15, 5, 16, 8], X[13, 20, 14, 21], 
 
  X[19, 15, 20, 22], X[21, 12, 22, 13], X[17, 9, 18, 14]]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Link[11, NonAlternating, 442]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[{1, -2, -4, 5}, {2, -1, -6, 7}, {-5, 4, -3, 10, -8, 11}, 
 
  {-7, 6, -11, 3, -9, 8, -10, 9}]</nowiki></pre></td></tr>
         <tr  valign=top><td><pre style="color: blue; border: 0px; padding:  0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red;  border: 0px; padding:  0em"><nowiki>Show[DrawMorseLink[Link[11, NonAlternating, 442]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L11n442_ML.gif]]</td></tr><tr valign=top><td><tt><font  color=blue>Out[6]=</font></tt><td><tt><font  color=black>-Graphics-</font></tt></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>KnotSignature[Link[11, NonAlternating, 442]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Link[11, NonAlternating, 442]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -3       5                       3/2       5/2       7/2       9/2
---- + ------- - 10 Sqrt[q] + 10 q    - 14 q    + 10 q    - 10 q    + 
 3/2   Sqrt[q]
q
 
     11/2      13/2    15/2
  6 q     - 3 q     + q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Link[11, NonAlternating, 442]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>    3    3    2       2       4       6       8       10      12
9 + -- + -- + -- + 7 q  + 11 q  + 13 q  + 10 q  + 12 q   + 5 q   + 
     6    4    2
    q    q    q
 
     14      16      18    20    22    24
  6 q   + 3 q   - 2 q   + q   - q   - q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Link[11, NonAlternating, 442]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>    1        3      3     a     1      5      10     9    3 a   z
-(-----) + ----- - ---- + -- + ---- - ---- + ---- - --- + --- + -- - 
   5  3     3  3      3    3    7      5      3     a z    z     7
  a  z     a  z    a z    z    a  z   a  z   a  z               a
 
                                 3      3      3      5
  6 z   13 z   11 z           3 z    7 z    5 z    2 z
  --- + ---- - ---- + 3 a z - ---- + ---- - ---- + ----
   5      3     a               5      3     a       3
  a      a                     a      a             a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Link[11, NonAlternating, 442]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>     -8   6    18   21     1       3      3     a    3      3
9 + a   + -- + -- + -- + ----- + ----- + ---- + -- - -- - ----- - 
           6    4    2    5  3    3  3      3    3    2    4  2
          a    a    a    a  z    a  z    a z    z    z    a  z
 
    6      2      11     18    14    5 a   6 z   30 z   49 z   35 z
  ----- - ---- - ---- - ---- - --- - --- + --- + ---- + ---- + ---- + 
   2  2    7      5      3     a z    z     7      5      3     a
  a  z    a  z   a  z   a  z               a      a      a
 
                     2       2       2       2      3       3       3
              2   3 z    14 z    28 z    24 z    9 z    47 z    74 z
  10 a z - 7 z  - ---- - ----- - ----- - ----- - ---- - ----- - ----- - 
                    8      6       4       2       7      5       3
                   a      a       a       a       a      a       a
 
      3                      4       4      4      4      5       5
  42 z         3      4   3 z    11 z    9 z    4 z    9 z    40 z
  ----- - 6 a z  + 3 z  + ---- + ----- + ---- + ---- + ---- + ----- + 
    a                       8      6       4      2      7      5
                           a      a       a      a      a      a
 
      5       5           6      6       6      6      7       7
  53 z    22 z       6   z    3 z    14 z    7 z    3 z    10 z
  ----- + ----- - 3 z  - -- + ---- + ----- + ---- - ---- - ----- - 
    3       a             8     6      4       2      7      5
   a                     a     a      a       a      a      a
 
      7      7      8      8      8    9    9
  14 z    7 z    3 z    8 z    5 z    z    z
  ----- - ---- - ---- - ---- - ---- - -- - --
    3      a       6      4      2     5    3
   a              a      a      a     a    a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Link[11, NonAlternating, 442]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       2     3       1     2    3        2        4        4  2
7 + 6 q  + ----- + ----- + - + ---- + 6 q  t + 4 q  t + 8 q  t  + 
            4  2    2  2   t    2
           q  t    q  t        q  t
 
     6  2      6  3      8  3      8  4      10  4      10  5
  9 q  t  + 5 q  t  + 5 q  t  + 5 q  t  + 6 q   t  + 2 q   t  + 
 
     12  5    12  6      14  6    16  7
  4 q   t  + q   t  + 2 q   t  + q   t</nowiki></pre></td></tr>
         </table> }}