View source for L10a111

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{{Link Page|
n = 10 |
t = a |
k = 111 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-10,5,-6,2,-3,7,-9:6,-1,9,-5,8,-2,4,-7,10,-8/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre">
<tr><td>[[Image:BraidPart3.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]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
khovanov_table  = <table border=1>
<tr align=center>
<td width=13.3333%><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=6.66667%>-6</td    ><td width=6.66667%>-5</td    ><td width=6.66667%>-4</td    ><td width=6.66667%>-3</td    ><td width=6.66667%>-2</td    ><td width=6.66667%>-1</td    ><td width=6.66667%>0</td    ><td width=6.66667%>1</td    ><td width=6.66667%>2</td    ><td width=6.66667%>3</td    ><td width=6.66667%>4</td    ><td width=13.3333%>&chi;</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>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>&nbsp;</td><td>-4</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>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>6</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>&nbsp;</td><td bgcolor=yellow>8</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>-4</td></tr>
<tr align=center><td>0</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>12</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>-2</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>0</td></tr>
<tr align=center><td>-4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>10</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</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>4</td></tr>
<tr align=center><td>-8</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</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>-6</td></tr>
<tr align=center><td>-10</td><td>&nbsp;</td><td bgcolor=yellow>1</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>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>-12</td><td bgcolor=yellow>&nbsp;</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>
<tr align=center><td>-14</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>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[10, Alternating, 111]]</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>10</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[10, Alternating, 111]]]</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[10, Alternating, 111]]</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[12, 1, 13, 2], X[16, 7, 17, 8], X[8, 3, 9, 4], X[2, 18, 3, 17], 
 
  X[14, 6, 15, 5], X[6, 12, 7, 11], X[18, 10, 19, 9], 
 
  X[20, 15, 11, 16], X[10, 13, 1, 14], X[4, 19, 5, 20]]</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[10, Alternating, 111]]</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, -4, 3, -10, 5, -6, 2, -3, 7, -9}, 
 
  {6, -1, 9, -5, 8, -2, 4, -7, 10, -8}]</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[10, Alternating, 111]]</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[4, {-1, 2, -3, 2, -1, -3, 2, -3, 2, -3}]</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[10, Alternating, 111]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L10a111_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[10, Alternating, 111]]</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>-1</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[10, Alternating, 111]][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>  -(13/2)     4      9      15     19     20      20
-q        + ----- - ---- + ---- - ---- + ---- - ------- + 15 Sqrt[q] - 
             11/2    9/2    7/2    5/2    3/2   Sqrt[q]
            q       q      q      q      q
 
      3/2      5/2    7/2
  11 q    + 5 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[10, Alternating, 111]][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>     -20    -18    -16    3     4     2    2    5    2       6      8
7 + q    - q    - q    + --- - --- + --- - -- + -- - -- + 3 q  - 3 q  + 
                          14    12    10    6    4    2
                         q     q     q     q    q    q
 
   10
  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[10, Alternating, 111]][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
   1     a            3      5     z         3      3  3    5  3   z
-(---) + - + a z - 2 a  z + a  z - -- + 3 a z  - 4 a  z  + a  z  - -- + 
  a z    z                         a                               a
 
       5      3  5      7
  3 a z  - 2 a  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>Kauffman[Link[10, Alternating, 111]][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>     1    a              3        5      2      2  2    4  2
1 - --- - - + 2 a z + 4 a  z + 2 a  z + z  + 2 a  z  - a  z  - 
    a z   z
 
               3                                                    4
     6  2   6 z          3       3  3      5  3    7  3      4   4 z
  2 a  z  - ---- - 19 a z  - 22 a  z  - 8 a  z  + a  z  - 2 z  + ---- - 
             a                                                     2
                                                                  a
 
                                  5       5
      2  4      4  4      6  4   z    17 z          5       3  5
  14 a  z  - 3 a  z  + 5 a  z  - -- + ----- + 39 a z  + 34 a  z  + 
                                  3     a
                                 a
 
                                6
      5  5    7  5       6   5 z        2  6       4  6      6  6
  12 a  z  - a  z  + 14 z  - ---- + 34 a  z  + 11 a  z  - 4 a  z  - 
                               2
                              a
 
      7
  11 z          7       3  7      5  7       8       2  8      4  8
  ----- - 15 a z  - 12 a  z  - 8 a  z  - 11 z  - 20 a  z  - 9 a  z  - 
    a
 
       9      3  9
  4 a z  - 4 a  z</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[10, Alternating, 111]][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>     10     1        3        1        6        3       9       6
12 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + 
      2    14  6    12  5    10  5    10  4    8  4    8  3    6  3
     q    q   t    q   t    q   t    q   t    q  t    q  t    q  t
 
   10       9      10     10             2        2  2      4  2
  ----- + ----- + ---- + ---- + 7 t + 8 q  t + 4 q  t  + 7 q  t  + 
   6  2    4  2    4      2
  q  t    q  t    q  t   q  t
 
   4  3      6  3    8  4
  q  t  + 4 q  t  + q  t</nowiki></pre></td></tr>
         </table> }}