View source for L11a444

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{{Link Page|
n = 11 |
t = a |
k = 444 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,4,-9,5,-6,3,-8:11,-2,7,-4,8,-5,6,-3,9,-7/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre">
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
</table> |
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%>-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=6.25%>6</td    ><td width=6.25%>7</td    ><td width=12.5%>&chi;</td></tr>
<tr align=center><td>17</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>15</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>13</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>11</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>9</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>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>7</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>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>8</td><td bgcolor=yellow>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>9</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>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>9</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>-1</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>-3</td><td>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>4</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>4</td></tr>
<tr align=center><td>-5</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>-7</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 September 3, 2005, 2:11:43)...</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, 444]]</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, 444]]]</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>3</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, 444]]</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[14, 3, 15, 4], X[20, 12, 21, 11], X[16, 8, 17, 7], 
 
  X[18, 10, 19, 9], X[10, 20, 11, 19], X[22, 16, 13, 15], 
 
  X[12, 18, 5, 17], X[8, 22, 9, 21], X[2, 5, 3, 6], X[4, 13, 1, 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, Alternating, 444]]</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, -10, 2, -11}, {10, -1, 4, -9, 5, -6, 3, -8}, 
 
  {11, -2, 7, -4, 8, -5, 6, -3, 9, -7}]</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>BR[Link[11, Alternating, 444]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[6, {1, 2, 2, 2, 3, 2, -1, 4, -3, 5, -4, -3, 2, -3, 4, -3, 2, -5, -4, 
 
   -3, 2}]</nowiki></pre></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>Show[DrawMorseLink[Link[11, Alternating, 444]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L11a444_ML.gif]]</td></tr><tr valign=top><td><tt><font  color=blue>Out[7]=</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[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>KnotSignature[Link[11, Alternating, 444]]</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>2</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>J=Jones[Link[11, Alternating, 444]][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   2    6              2       3       4       5      6
-9 + q   - -- + - + 14 q - 17 q  + 18 q  - 15 q  + 13 q  - 8 q  + 
            2   q
           q
 
     7    8
  4 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>A2Invariant[Link[11, Alternating, 444]][q]</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>     -10    -8   3       2    4      6      8      10      12    14
1 + q    + q   + -- + 5 q  - q  + 5 q  + 2 q  + 3 q   + 5 q   - q   + 
                  4
                 q
 
     16    18    20      22    24
  4 q   - q   - q   + 2 q   - q</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>HOMFLYPT[Link[11, Alternating, 444]][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>                                               2      2      2
3    5       2    -2     1       2        2   z    2 z    3 z
-- - -- + 2 a  + z   + ----- - ----- - 4 z  - -- + ---- - ---- + 
 4    2                 4  2    2  2           6     4      2
a    a                 a  z    a  z           a     a      a
 
                  4      4    4    6    6
   2  2      4   z    2 z    z    z    z
  a  z  - 2 z  - -- + ---- + -- + -- + --
                  6     4     2    4    2
                 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>Kauffman[Link[11, Alternating, 444]][a, z]</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    9       2    -2     1       2      2      2    z    8 z
3 - -- + -- + -- - 2 a  - z   - ----- - ----- + ---- + --- + -- - --- - 
     6    4    2                 4  2    2  2    3     a z    5    3
    a    a    a                 a  z    a  z    a  z         a    a
 
                        2      2      2       2              3      3
  8 z            2   2 z    2 z    5 z    15 z       2  2   z    3 z
  --- + a z - 5 z  + ---- + ---- - ---- - ----- + 5 a  z  - -- + ---- + 
   a                   8      6      4      2                9     7
                      a      a      a      a                a     a
 
     3       3       3                      4    4       4       4
  3 z    13 z    16 z         3      4   6 z    z    12 z    15 z
  ---- + ----- + ----- + 2 a z  + 6 z  - ---- + -- + ----- + ----- - 
    5      3       a                       8     6     4       2
   a      a                               a     a     a       a
 
             5       5      5      5       5                      6
     2  4   z    11 z    8 z    5 z    14 z         5      6   4 z
  4 a  z  + -- - ----- - ---- - ---- - ----- - 5 a z  - 7 z  + ---- - 
             9     7       5      3      a                       8
            a     a       a      a                              a
 
     6       6       6              7    7      7      7
  9 z    18 z    13 z     2  6   7 z    z    6 z    2 z         7
  ---- - ----- - ----- + a  z  + ---- + -- - ---- + ---- + 2 a z  + 
    6      4       2               7     5     3     a
   a      a       a               a     a     a
 
            8      8      8      9      9      9    10    10
     8   7 z    9 z    5 z    4 z    6 z    2 z    z     z
  3 z  + ---- + ---- + ---- + ---- + ---- + ---- + --- + ---
           6      4      2      5      3     a      4     2
          a      a      a      a      a            a     a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Link[11, Alternating, 444]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>         3     1       1       2       4      2      5    4 q
9 q + 6 q  + ----- + ----- + ----- + ----- + ---- + --- + --- + 
              7  4    5  4    5  3    3  2      2   q t    t
             q  t    q  t    q  t    q  t    q t
 
     3        5        5  2      7  2      7  3      9  3      9  4
  9 q  t + 8 q  t + 9 q  t  + 9 q  t  + 6 q  t  + 9 q  t  + 7 q  t  + 
 
     11  4      11  5      13  5    13  6      15  6    17  7
  8 q   t  + 3 q   t  + 5 q   t  + q   t  + 3 q   t  + q   t</nowiki></pre></td></tr>
         </table> }}