View source for K11a252

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{{Hoste-Thistlethwaite Knot Page|
n = 11 |
t = a |
k = 252 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-7,3,-1,4,-2,5,-11,6,-3,7,-10,8,-6,9,-5,10,-8,11,-9/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]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
same_alexander  = [[K11a131]], [[K11a254]],  |
same_jones      = [[K11a254]],  |
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%>-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=6.25%>6</td    ><td width=12.5%>&chi;</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>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&nbsp;</td><td>-3</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>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>-6</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>&nbsp;</td><td bgcolor=yellow>10</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>11</td><td bgcolor=yellow>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>3</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>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>8</td><td bgcolor=yellow>12</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>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</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>-4</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</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>&nbsp;</td><td>&nbsp;</td><td>6</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</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>-4</td></tr>
<tr align=center><td>-7</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>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-9</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> |
coloured_jones_2 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_3 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_4 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> |
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[Knot[11, Alternating, 252]]</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>PD[Knot[11, Alternating, 252]]</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>PD[X[6, 2, 7, 1], X[8, 4, 9, 3], X[12, 5, 13, 6], X[2, 8, 3, 7], 
 
  X[18, 9, 19, 10], X[16, 12, 17, 11], X[4, 13, 5, 14], 
 
  X[20, 16, 21, 15], X[22, 17, 1, 18], X[14, 20, 15, 19], 
 
  X[10, 21, 11, 22]]</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>GaussCode[Knot[11, Alternating, 252]]</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>GaussCode[1, -4, 2, -7, 3, -1, 4, -2, 5, -11, 6, -3, 7, -10, 8, -6, 9, 
 
  -5, 10, -8, 11, -9]</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>BR[Knot[11, Alternating, 252]]</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>BR[4, {-1, 2, 2, 2, -1, -3, 2, 2, -3, 2, -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[Knot[11, Alternating, 252]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:K11a252_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>alex = Alexander[Knot[11, Alternating, 252]][t]</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>       -4   6    16   27              2      3    4
-31 - t   + -- - -- + -- + 27 t - 16 t  + 6 t  - t
             3    2   t
            t    t</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>Conway[Knot[11, Alternating, 252]][z]</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      6    8
1 + z  - 2 z  - z</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>Select[AllKnots[], (alex === Alexander[#][t])&]</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>{Knot[11, Alternating, 131], Knot[11, Alternating, 252], 
 
  Knot[11, Alternating, 254]}</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>{KnotDet[Knot[11, Alternating, 252]], KnotSignature[Knot[11, Alternating, 252]]}</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>{131, 2}</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>J=Jones[Knot[11, Alternating, 252]][q]</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>       -4   3    7    13              2       3       4      5      6
-17 - q   + -- - -- + -- + 21 q - 21 q  + 19 q  - 15 q  + 9 q  - 4 q  + 
             3    2   q
            q    q
 
   7
  q</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>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</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>{Knot[11, Alternating, 252], Knot[11, Alternating, 254]}</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>A2Invariant[Knot[11, Alternating, 252]][q]</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>     -12   2    4     -2      2      4      6      8      10    12
3 - q    - -- + -- - q   + 3 q  - 3 q  + 4 q  - 5 q  + 2 q   - q   - 
            6    4
           q    q
 
     14      16      18    20
  2 q   + 3 q   - 2 q   + q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[11, Alternating, 252]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                                    2
     -4   4       2   2 z   6 z   7 z              3         2   2 z
6 + a   + -- + 2 a  - --- - --- - --- - 5 a z - 2 a  z - 22 z  + ---- - 
           2           5     3     a                               6
          a           a     a                                     a
 
     2       2              3       3       3       3
  3 z    19 z       2  2   z    11 z    23 z    15 z         3
  ---- - ----- - 8 a  z  - -- + ----- + ----- + ----- + 9 a z  + 
    4      2                7     5       3       a
   a      a                a     a       a
 
                     4      4       4       4                 5
     3  3       4   z    7 z    10 z    47 z        2  4   4 z
  5 a  z  + 43 z  + -- - ---- + ----- + ----- + 14 a  z  + ---- - 
                     8     6      4       2                  7
                    a     a      a       a                  a
 
      5       5      5                                 6       6
  20 z    27 z    3 z         5      3  5       6   9 z    22 z
  ----- - ----- + ---- + 2 a z  - 4 a  z  - 35 z  + ---- - ----- - 
    5       3      a                                  6      4
   a       a                                         a      a
 
      6                  7    7       7
  55 z        2  6   14 z    z    26 z          7    3  7      8
  ----- - 11 a  z  + ----- - -- - ----- - 10 a z  + a  z  + 6 z  + 
    2                  5      3     a
   a                  a      a
 
      8       8                9       9                       10
  14 z    17 z       2  8   8 z    12 z         9      10   2 z
  ----- + ----- + 3 a  z  + ---- + ----- + 4 a z  + 2 z   + -----
    4       2                 3      a                        2
   a       a                 a                               a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[11, Alternating, 252]], Vassiliev[3][Knot[11, Alternating, 252]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{1, -1}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[11, Alternating, 252]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>           3     1       2       1       5       2       8      5
12 q + 10 q  + ----- + ----- + ----- + ----- + ----- + ----- + ---- + 
                9  5    7  4    5  4    5  3    3  3    3  2      2
               q  t    q  t    q  t    q  t    q  t    q  t    q t
 
   9    8 q       3         5        5  2       7  2      7  3
  --- + --- + 10 q  t + 11 q  t + 9 q  t  + 10 q  t  + 6 q  t  + 
  q t    t
 
     9  3      9  4      11  4    11  5      13  5    15  6
  9 q  t  + 3 q  t  + 6 q   t  + q   t  + 3 q   t  + q   t</nowiki></pre></td></tr>
         </table> }}