View source for L10a174

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{{Link Page|
n = 10 |
t = a |
k = 174 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,4,-5:2,-1,6,-7:5,-4,3,-10:7,-6,8,-9:10,-3,9,-8/goTop.html |
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%>-10</td    ><td width=6.66667%>-9</td    ><td width=6.66667%>-8</td    ><td width=6.66667%>-7</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=13.3333%>&chi;</td></tr>
<tr align=center><td>-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>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>6</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>4</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>0</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 bgcolor=yellow>11</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>-13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>10</td><td bgcolor=yellow>14</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>-15</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>-17</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</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>9</td></tr>
<tr align=center><td>-19</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</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>0</td></tr>
<tr align=center><td>-21</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>-23</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&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>0</td></tr>
<tr align=center><td>-25</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 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[10, Alternating, 174]]</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, 174]]]</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>5</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, 174]]</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[2, 5, 3, 6], X[18, 11, 19, 12], X[10, 3, 11, 4], 
 
  X[4, 9, 1, 10], X[14, 7, 15, 8], X[8, 13, 5, 14], X[20, 15, 17, 16], 
 
  X[16, 19, 13, 20], X[12, 17, 9, 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[10, Alternating, 174]]</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, -2, 4, -5}, {2, -1, 6, -7}, {5, -4, 3, -10}, 
 
  {7, -6, 8, -9}, {10, -3, 9, -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>Show[DrawMorseLink[Link[10, Alternating, 174]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:L10a174_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[10, Alternating, 174]]</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</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[10, Alternating, 174]][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> -12    -11    6    6    15   11   15   10   10   4     -2
q    - q    + --- - -- + -- - -- + -- - -- + -- - -- + q
               10    9    8    7    6    5    4    3
              q     q    q    q    q    q    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[10, Alternating, 174]][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> -40    5    10    15    25    31    30    35    29    23    18
q    + --- + --- + --- + --- + --- + --- + --- + --- + --- + --- + 
        38    36    34    32    30    28    26    24    22    20
       q     q     q     q     q     q     q     q     q     q
 
   8     9     -14    2     3    3     -6
  --- + --- + q    + --- + --- - -- + q
   18    16           12    10    8
  q     q            q     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[10, Alternating, 174]][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>                          6      8      10      12    14      6
    6       8       10   a    4 a    6 a     4 a     a     5 a
10 a  - 20 a  + 10 a   + -- - ---- + ----- - ----- + --- + ---- - 
                          4     4      4       4      4      2
                         z     z      z       z      z      z
 
      8       10      12
  15 a    15 a     5 a         6  2       8  2    4  4      6  4
  ----- + ------ - ----- + 10 a  z  - 10 a  z  + a  z  + 4 a  z
    2        2       2
   z        z       z</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[10, Alternating, 174]][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>                                             6      8      10      12
     6       8       10       12       14   a    4 a    6 a     4 a
-10 a  - 25 a  - 31 a   - 25 a   - 10 a   - -- - ---- - ----- - ----- - 
                                             4     4      4       4
                                            z     z      z       z
 
   14      7       9       11      13      6       8       10
  a     4 a    12 a    12 a     4 a     5 a    14 a    18 a
  --- + ---- + ----- + ------ + ----- + ---- + ----- + ------ + 
   4      3      3        3       3       2      2        2
  z      z      z        z       z       z      z        z
 
      12      14       7       9       11       13
  14 a     5 a     15 a    41 a    41 a     15 a         7
  ------ + ----- - ----- - ----- - ------ - ------ + 20 a  z + 
     2       2       z       z       z        z
    z       z
 
      9         11         13         6  2       8  2       10  2
  55 a  z + 55 a   z + 20 a   z + 10 a  z  + 30 a  z  + 40 a   z  + 
 
      12  2       14  2       7  3       9  3       11  3       13  3
  30 a   z  + 10 a   z  - 10 a  z  - 30 a  z  - 30 a   z  - 10 a   z  + 
 
   4  4       6  4       8  4       10  4       12  4      14  4
  a  z  - 14 a  z  - 25 a  z  - 25 a   z  - 20 a   z  - 5 a   z  + 
 
     5  5       7  5       9  5      11  5       6  6      8  6
  4 a  z  - 10 a  z  - 12 a  z  + 2 a   z  + 10 a  z  + 5 a  z  - 
 
     10  6      12  6    14  6       7  7       9  7      11  7
  2 a   z  + 4 a   z  + a   z  + 10 a  z  + 11 a  z  + 2 a   z  + 
 
   13  7      8  8      10  8    12  8    9  9    11  9
  a   z  + 5 a  z  + 6 a   z  + a   z  + 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>Kh[Link[10, Alternating, 174]][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> -5    -3      1        1        6        5        5        1
q   + q   + ------- + ------ + ------ + ------ + ------ + ------ + 
             25  10    21  9    21  8    19  8    19  7    17  7
            q   t     q   t    q   t    q   t    q   t    q   t
 
    10       5        1        10       14       11       6
  ------ + ------ + ------ + ------ + ------ + ------ + ------ + 
   17  6    15  6    15  5    13  5    13  4    11  4    11  3
  q   t    q   t    q   t    q   t    q   t    q   t    q   t
 
    4       4       6      4
  ----- + ----- + ----- + ----
   9  3    9  2    7  2    5
  q  t    q  t    q  t    q  t</nowiki></pre></td></tr>
         </table> }}