View source for L11a240

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{{Link Page|
n = 11 |
t = a |
k = 240 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10,5,-11:9,-1,3,-4,10,-2,4,-8,7,-6,11,-5,8,-7,6,-3/goTop.html |
khovanov_table  = <table border=1>
<tr align=center>
<td width=12.5%><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=6.25%>-6</td    ><td width=6.25%>-5</td    ><td width=6.25%>-4</td    ><td width=6.25%>-3</td    ><td width=6.25%>-2</td    ><td width=6.25%>-1</td    ><td width=6.25%>0</td    ><td width=6.25%>1</td    ><td width=6.25%>2</td    ><td width=6.25%>3</td    ><td width=6.25%>4</td    ><td width=6.25%>5</td    ><td width=12.5%>&chi;</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&nbsp;</td><td>3</td></tr>
<tr align=center><td>8</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>5</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-4</td></tr>
<tr align=center><td>6</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>8</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>4</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>9</td><td bgcolor=yellow>5</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>0</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>10</td><td bgcolor=yellow>10</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>10</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>-6</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>5</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>
<tr align=center><td>-8</td><td>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>5</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>5</td></tr>
<tr align=center><td>-10</td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</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>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-12</td><td bgcolor=yellow>1</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>&nbsp;</td><td>&nbsp;</td><td>1</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, Alternating, 240]]</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, Alternating, 240]]]</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>2</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, Alternating, 240]]</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[8, 1, 9, 2], X[12, 3, 13, 4], X[22, 10, 7, 9], X[10, 14, 11, 13], 
 
  X[18, 5, 19, 6], X[16, 22, 17, 21], X[20, 16, 21, 15], 
 
  X[14, 20, 15, 19], X[2, 7, 3, 8], X[4, 11, 5, 12], X[6, 17, 1, 18]]</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, Alternating, 240]]</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, -9, 2, -10, 5, -11}, 
 
  {9, -1, 3, -4, 10, -2, 4, -8, 7, -6, 11, -5, 8, -7, 6, -3}]</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, Alternating, 240]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L11a240_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, Alternating, 240]]</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, Alternating, 240]][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>  -(11/2)    2      7      10     15      18
-q        + ---- - ---- + ---- - ---- + ------- - 18 Sqrt[q] + 
             9/2    7/2    5/2    3/2   Sqrt[q]
            q      q      q      q
 
      3/2       5/2      7/2      9/2    11/2
  17 q    - 13 q    + 8 q    - 4 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, Alternating, 240]][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>      -18    2     -14    4     3    4    3     -2      2      4
-1 + q    + --- + q    + --- + --- + -- - -- - q   - 4 q  + 3 q  - 
             16           12    10    6    4
            q            q     q     q    q
 
     6      8    10      12      14    16
  3 q  + 3 q  + q   - 2 q   + 2 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, Alternating, 240]][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>       3      5                                         3      3
a   3 a    2 a    z    5 z              3      5     2 z    7 z
- - ---- + ---- + -- - --- + 7 a z - 7 a  z + a  z + ---- - ---- + 
z    z      z      3    a                              3     a
                  a                                   a
 
                      5      5             7
       3      3  3   z    4 z         5   z
  9 a z  - 3 a  z  + -- - ---- + 3 a z  - --
                      3    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, Alternating, 240]][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>                         3      5
       2      4   a   3 a    2 a    z    3 z      3        5
1 + 3 a  + 3 a  - - - ---- - ---- + -- + --- + 5 a  z + 7 a  z + 
                  z    z      z      3    a
                                    a
 
             2    2                          3      3       3
      2   2 z    z       2  2      4  2   2 z    6 z    23 z
  13 z  - ---- - -- + 8 a  z  - 4 a  z  + ---- - ---- - ----- - 
            4     2                         5      3      a
           a     a                         a      a
 
                                        4      4    4
       3      3  3      5  3       4   z    7 z    z        2  4
  9 a z  - 3 a  z  - 9 a  z  - 41 z  - -- + ---- - -- - 35 a  z  - 
                                        6     4     2
                                       a     a     a
 
               5       5       5
     4  4   4 z    14 z    32 z         5      3  5      5  5       6
  3 a  z  - ---- + ----- + ----- + 5 a z  - 4 a  z  + 5 a  z  + 48 z  - 
              5      3       a
             a      a
 
     6       6                            7      7
  8 z    12 z        2  6      4  6   11 z    6 z          7
  ---- + ----- + 34 a  z  + 6 a  z  - ----- - ---- + 14 a z  + 
    4      2                            3      a
   a      a                            a
 
                                8                          9
     3  7    5  7       8   10 z       2  8      4  8   5 z         9
  8 a  z  - a  z  - 16 z  - ----- - 8 a  z  - 2 a  z  - ---- - 8 a z  - 
                              2                          a
                             a
 
     3  9    10    2  10
  3 a  z  - z   - a  z</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, Alternating, 240]][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     1        1        2        5       2       5       5
10 + 9 q  + ------ + ------ + ------ + ----- + ----- + ----- + ----- + 
             12  6    10  6    10  5    8  4    6  4    6  3    4  3
            q   t    q   t    q   t    q  t    q  t    q  t    q  t
 
   10       5     10    8        2        4        4  2      6  2
  ----- + ----- + -- + ---- + 8 q  t + 9 q  t + 5 q  t  + 8 q  t  + 
   4  2    2  2   t     2
  q  t    q  t         q  t
 
     6  3      8  3    8  4      10  4    12  5
  3 q  t  + 5 q  t  + q  t  + 3 q   t  + q   t</nowiki></pre></td></tr>
         </table> }}