T(11,4) - Revision history

ScottKnotPageRobot at 15:37, 31 August 2005

2005-08-31T15:37:33Z

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-<!-- This page was  generated from the splice template "Torus_Knot_Splice_Template". Please do not edit! -->
+<!-- This page was generated from the splice template [[Torus_Knot_Splice_Base]]. Please do not edit!
 {{Torus Knot Page|
 m = 11 |

ScottKnotPageRobot at 16:15, 30 August 2005

2005-08-30T16:15:13Z

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ScottTestRobot at 00:44, 29 August 2005

2005-08-29T00:44:55Z

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ScottTestRobot at 23:42, 28 August 2005

2005-08-28T23:42:27Z

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 |- valign=top
 |[[Image:{{PAGENAME}}.jpg]]
-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-30,-32,-1,4,5,6,-9,-11,-13,16,17,18,-21,-23,-25,28,29,30,-33,-2,-4,7,8,9,-12,-14,-16,19,20,21,-24,-26,-28,31,32,33,-3,-5,-7,10,11,12,-15,-17,-19,22,23,24,-27,-29,-31,1,2,3,-6,-8,-10,13,14,15,-18,-20,-22,25,26,27/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=11|n=4|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-30,-32,-1,4,5,6,-9,-11,-13,16,17,18,-21,-23,-25,28,29,30,-33,-2,-4,7,8,9,-12,-14,-16,19,20,21,-24,-26,-28,31,32,33,-3,-5,-7,10,11,12,-15,-17,-19,22,23,24,-27,-29,-31,1,2,3,-6,-8,-10,13,14,15,-18,-20,-22,25,26,27/goTop.html}}
 {{:{{PAGENAME}} Quick Notes}}
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 {{Knot Presentations}}
 {{Polynomial Invariants}}
 {{Vassiliev Invariants}}
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   q   t   + q   t   + q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:25, 28 August 2005

2005-08-28T01:25:38Z

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DrorsRobot at 02:47, 27 August 2005

2005-08-27T02:47:17Z

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DrorsRobot at 02:19, 27 August 2005

2005-08-27T02:19:50Z

New page

{{Knot Navigation Links|prev=T(16,3).jpg|next=T(33,2).jpg}}

Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-30,-32,-1,4,5,6,-9,-11,-13,16,17,18,-21,-23,-25,28,29,30,-33,-2,-4,7,8,9,-12,-14,-16,19,20,21,-24,-26,-28,31,32,33,-3,-5,-7,10,11,12,-15,-17,-19,22,23,24,-27,-29,-31,1,2,3,-6,-8,-10,13,14,15,-18,-20,-22,25,26,27/goTop.html T(11,4)'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!

Visit [http://www.math.toronto.edu/~drorbn/KAtlas/TorusKnots/11.4.html T(11,4)'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]!

===Knot presentations===

{|
|'''[[Planar Diagrams|Planar diagram presentation]]'''
|style="padding-left: 1em;" | X3,53,4,52 X20,54,21,53 X37,55,38,54 X21,5,22,4 X38,6,39,5 X55,7,56,6 X39,23,40,22 X56,24,57,23 X7,25,8,24 X57,41,58,40 X8,42,9,41 X25,43,26,42 X9,59,10,58 X26,60,27,59 X43,61,44,60 X27,11,28,10 X44,12,45,11 X61,13,62,12 X45,29,46,28 X62,30,63,29 X13,31,14,30 X63,47,64,46 X14,48,15,47 X31,49,32,48 X15,65,16,64 X32,66,33,65 X49,1,50,66 X33,17,34,16 X50,18,51,17 X1,19,2,18 X51,35,52,34 X2,36,3,35 X19,37,20,36
|-
|'''[[Gauss Codes|Gauss code]]'''
|style="padding-left: 1em;" | {-30, -32, -1, 4, 5, 6, -9, -11, -13, 16, 17, 18, -21, -23, -25, 28, 29, 30, -33, -2, -4, 7, 8, 9, -12, -14, -16, 19, 20, 21, -24, -26, -28, 31, 32, 33, -3, -5, -7, 10, 11, 12, -15, -17, -19, 22, 23, 24, -27, -29, -31, 1, 2, 3, -6, -8, -10, 13, 14, 15, -18, -20, -22, 25, 26, 27}
|-
|'''[[DT (Dowker-Thistlethwaite) Codes|Dowker-Thistlethwaite code]]'''
|style="padding-left: 1em;" | 18 52 -38 24 58 -44 30 64 -50 36 4 -56 42 10 -62 48 16 -2 54 22 -8 60 28 -14 66 34 -20 6 40 -26 12 46 -32
|}

===Polynomial invariants===

{{Polynomial Invariants|name=T(11,4)}}

===[[Finite Type (Vassiliev) Invariants|Vassiliev invariants]]===
{| style="margin-left: 1em;"
|-
|'''V2 and V3'''
|style="padding-left: 1em;" | {0, 550})
|}

[[Khovanov Homology]]. The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with yellow highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>22 is the signature of T(11,4). Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

<center><table border=1>
<tr align=center>
<td width=7.69231%><table cellpadding=0 cellspacing=0>
<tr><td>\</td><td> </td><td>r</td></tr>
<tr><td> </td><td> \ </td><td> </td></tr>
<tr><td>j</td><td> </td><td>\</td></tr>
</table></td>
<td width=3.84615%>0</td ><td width=3.84615%>1</td ><td width=3.84615%>2</td ><td width=3.84615%>3</td ><td width=3.84615%>4</td ><td width=3.84615%>5</td ><td width=3.84615%>6</td ><td width=3.84615%>7</td ><td width=3.84615%>8</td ><td width=3.84615%>9</td ><td width=3.84615%>10</td ><td width=3.84615%>11</td ><td width=3.84615%>12</td ><td width=3.84615%>13</td ><td width=3.84615%>14</td ><td width=3.84615%>15</td ><td width=3.84615%>16</td ><td width=3.84615%>17</td ><td width=3.84615%>18</td ><td width=3.84615%>19</td ><td width=3.84615%>20</td ><td width=3.84615%>21</td ><td width=7.69231%>χ</td></tr>
<tr align=center><td>63</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>0</td></tr>
<tr align=center><td>61</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td>0</td></tr>
<tr align=center><td>59</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td bgcolor=red>1</td><td> </td><td>0</td></tr>
<tr align=center><td>57</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>55</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>53</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>51</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>2</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>49</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>47</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>45</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>43</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>41</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td bgcolor=red>1</td><td bgcolor=red>2</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>39</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>37</td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td> </td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>35</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>33</td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>31</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>29</td><td bgcolor=red>1</td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
</table></center>

{{Computer Talk Header}}

<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=    </pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 19, 2005, 13:11:25)...</pre></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[TorusKnot[11, 4]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>33</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[TorusKnot[11, 4]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[3, 53, 4, 52], X[20, 54, 21, 53], X[37, 55, 38, 54],

X[21, 5, 22, 4], X[38, 6, 39, 5], X[55, 7, 56, 6], X[39, 23, 40, 22],

X[56, 24, 57, 23], X[7, 25, 8, 24], X[57, 41, 58, 40],

X[8, 42, 9, 41], X[25, 43, 26, 42], X[9, 59, 10, 58],

X[26, 60, 27, 59], X[43, 61, 44, 60], X[27, 11, 28, 10],

X[44, 12, 45, 11], X[61, 13, 62, 12], X[45, 29, 46, 28],

X[62, 30, 63, 29], X[13, 31, 14, 30], X[63, 47, 64, 46],

X[14, 48, 15, 47], X[31, 49, 32, 48], X[15, 65, 16, 64],

X[32, 66, 33, 65], X[49, 1, 50, 66], X[33, 17, 34, 16],

X[50, 18, 51, 17], X[1, 19, 2, 18], X[51, 35, 52, 34],

X[2, 36, 3, 35], X[19, 37, 20, 36]]</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[TorusKnot[11, 4]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[-30, -32, -1, 4, 5, 6, -9, -11, -13, 16, 17, 18, -21, -23,

-25, 28, 29, 30, -33, -2, -4, 7, 8, 9, -12, -14, -16, 19, 20, 21,

-24, -26, -28, 31, 32, 33, -3, -5, -7, 10, 11, 12, -15, -17, -19, 22,

23, 24, -27, -29, -31, 1, 2, 3, -6, -8, -10, 13, 14, 15, -18, -20,

-22, 25, 26, 27]</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[TorusKnot[11, 4]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3,

1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 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>alex = Alexander[TorusKnot[11, 4]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -15 -14 -11 -10 -7 -6 -4 -2 2 4 6
1 + t - t + t - t + t - t + t - t - t + t - t +

7 10 11 14 15
t - t + t - t + t</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>Conway[TorusKnot[11, 4]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12
1 + 75 z + 1510 z + 12825 z + 56577 z + 148070 z + 249288 z +

14 16 18 20 22
283951 z + 225760 z + 127470 z + 51380 z + 14675 z +

24 26 28 30
2900 z + 377 z + 29 z + z</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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</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>{KnotDet[TorusKnot[11, 4]], KnotSignature[TorusKnot[11, 4]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{11, 22}</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>J=Jones[TorusKnot[11, 4]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 15 17 19 20 21 22 23 24 25 26 28
q + q + q - 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[11]:=</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[11]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</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>A2Invariant[TorusKnot[11, 4]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>NotAvailable</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>Kauffman[TorusKnot[11, 4]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>NotAvailable</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>{Vassiliev[2][TorusKnot[11, 4]], Vassiliev[3][TorusKnot[11, 4]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 550}</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>Kh[TorusKnot[11, 4]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 29 31 33 2 37 3 35 4 37 4 39 5 41 5
q + q + q t + q t + q t + q t + q t + q t +

37 6 39 6 41 7 43 7 41 8 45 9 43 10
q t + q t + q t + q t + 2 q t + 2 q t + q t +

45 10 47 11 49 11 45 12 47 12 51 12
q t + 2 q t + q t + q t + 2 q t + q t +

49 13 51 13 49 14 53 15 51 16 53 16
q t + 2 q t + 2 q t + 3 q t + q t + 2 q t +

57 16 55 17 57 17 55 18 59 18 59 19
q t + 2 q t + 2 q t + q t + q t + 2 q t +

59 20 63 20 63 21
q t + q t + q t</nowiki></pre></td></tr>
</table>