View source for L11n319

<!--                       WARNING! WARNING! WARNING!
<!-- This page was generated from the splice template [[Link_Splice_Base]]. Please do not edit!
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link_Splice_Base]]. -->
<!-- <math>\text{Null}</math> -->
<!-- <math>\text{Null}</math> -->
<!--                       WARNING! WARNING! WARNING!
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit!
<!-- Almost certainly, you want to edit [[Template:Link Page]], which actually produces this page.
<!-- The text below simply calls [[Template:Link Page]] setting the values of all the parameters appropriately.
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link Splice Template]]. -->
<!-- <math>\text{Null}</math> -->
{{Link Page|
n = 11 |
t = n |
k = 319 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:3,-1,9,-8,10,-7:-4,-2,7,-3,11,6,-5,-9,8,4,-6,5/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:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
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%>-4</td    ><td width=7.14286%>-3</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=14.2857%>&chi;</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>2</td><td>-2</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>2</td><td bgcolor=yellow>&nbsp;</td><td>2</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>5</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>-3</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>5</td><td bgcolor=yellow>2</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>5</td><td bgcolor=yellow>6</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>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</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>-1</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td bgcolor=yellow>1</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>3</td></tr>
<tr align=center><td>-5</td><td bgcolor=yellow>&nbsp;</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>-2</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>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, NonAlternating, 319]]</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, 319]]]</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, NonAlternating, 319]]</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[12, 4, 13, 3], X[14, 5, 15, 6], X[11, 21, 12, 20], 
 
  X[17, 11, 18, 22], X[21, 17, 22, 16], X[10, 13, 5, 14], 
 
  X[8, 20, 9, 19], X[18, 8, 19, 7], X[2, 9, 3, 10], X[4, 16, 1, 15]]</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, 319]]</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}, {3, -1, 9, -8, 10, -7}, 
 
  {-4, -2, 7, -3, 11, 6, -5, -9, 8, 4, -6, 5}]</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, NonAlternating, 319]]</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, -3, 2, 1, 1, -3, 2, 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[11, NonAlternating, 319]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L11n319_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, NonAlternating, 319]]</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, NonAlternating, 319]][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    6             2       3      4      5      6
-7 + q   - -- + - + 11 q - 9 q  + 10 q  - 7 q  + 4 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>A2Invariant[Link[11, NonAlternating, 319]][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>     -8    -6   2     -2      2      4       6      8      10    12
4 + q   - q   + -- + q   + 7 q  + 5 q  + 10 q  + 3 q  + 4 q   - q   - 
                 4
                q
 
     14    16      18    22
  3 q   - q   - 3 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, NonAlternating, 319]][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    8    10   2      1       4       5        2   z    9 z
4 - -- + -- - -- + -- - ----- + ----- - ----- + 5 z  - -- + ---- - 
     6    4    2    2    6  2    4  2    2  2           6     4
    a    a    a    z    a  z    a  z    a  z           a     a
 
      2             4       4         6      6    8
  14 z       4   5 z    13 z     6   z    6 z    z
  ----- + 4 z  + ---- - ----- + z  + -- - ---- - --
    2              4      2           4     2     2
   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>Kauffman[Link[11, NonAlternating, 319]][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>    3    12   15   2      1       4       5      1      5      9
7 + -- + -- + -- - -- - ----- - ----- - ----- + ---- + ---- + ---- + 
     6    4    2    2    6  2    4  2    2  2    7      5      3
    a    a    a    z    a  z    a  z    a  z    a  z   a  z   a  z
 
                                              2       2       2
   5    5 z   18 z   24 z   11 z       2   4 z    26 z    37 z
  --- - --- - ---- - ---- - ---- - 13 z  - ---- - ----- - ----- + 
  a z    7      5      3     a               6      4       2
        a      a      a                     a      a       a
 
               3       3       3       3                       4
     2  2   3 z    25 z    31 z    14 z         3       4   2 z
  2 a  z  + ---- + ----- + ----- + ----- + 5 a z  + 14 z  + ---- + 
              7      5       3       a                        6
             a      a       a                                a
 
      4       4                 5       5       5
  35 z    50 z       2  4   13 z    15 z    11 z         5       6
  ----- + ----- - 3 a  z  - ----- - ----- - ----- - 9 a z  - 13 z  + 
    4       2                 5       3       a
   a       a                 a       a
 
   6       6       6              7    7                      8
  z    19 z    34 z     2  6   4 z    z         7      8   5 z
  -- - ----- - ----- + a  z  + ---- - -- + 3 a z  + 4 z  + ---- + 
   6     4       2               5    a                      4
  a     a       a               a                           a
 
     8      9      9
  9 z    2 z    2 z
  ---- + ---- + ----
    2      3     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, NonAlternating, 319]][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       2       1       4      3      4    3 q
7 q + 6 q  + ----- + ----- + ----- + ----- + ---- + --- + --- + 
              7  4    5  3    3  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
  4 q  t + 5 q  t + 6 q  t  + 5 q  t  + 2 q  t  + 5 q  t  + 2 q  t  + 
 
     11  4      13  5
  2 q   t  + 2 q   t</nowiki></pre></td></tr>
         </table> }}