View source for 10 28

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{{Knot Navigation Links|ext=gif}}

{{Rolfsen Knot Page Header|n=10|k=28|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-6,7,-10,2,-8,9,-3,4,-7,6,-5,3,-9,8/goTop.html}}

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{{:{{PAGENAME}} Further Notes and Views}}

{{Knot Presentations}}

<center><table border=1 cellpadding=10><tr align=center valign=top>
<td>
[[Braid Representatives|Minimum Braid Representative]]:
<table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
</table>

[[Invariants from Braid Theory|Length]] is 12, width is 5.

[[Invariants from Braid Theory|Braid index]] is 5.
</td>
<td>
[[Lightly Documented Features|A Morse Link Presentation]]:

[[Image:{{PAGENAME}}_ML.gif]]
</td>
</tr></table></center>

{{3D Invariants}}
{{4D Invariants}}
{{Polynomial Invariants}}

=== "Similar" Knots (within the Atlas) ===

Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]:
{[[10_37]], ...}

Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): 
{...}

{{Vassiliev Invariants}}

{{Khovanov Homology|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%>-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=6.66667%>5</td  ><td width=6.66667%>6</td  ><td width=6.66667%>7</td  ><td width=13.3333%>&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 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 bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</td><td>1</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>3</td><td bgcolor=yellow>1</td><td>&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>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>2</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>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</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 bgcolor=yellow>5</td><td bgcolor=yellow>3</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 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>1</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</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>-1</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</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>2</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td bgcolor=yellow>1</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>-2</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>&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>&nbsp;</td><td>-1</td></tr>
</table>}}

{{Display Coloured Jones|J2=<math>q^{21}-2 q^{20}-q^{19}+7 q^{18}-5 q^{17}-9 q^{16}+18 q^{15}-4 q^{14}-24 q^{13}+29 q^{12}+4 q^{11}-41 q^{10}+34 q^9+16 q^8-53 q^7+32 q^6+26 q^5-54 q^4+23 q^3+29 q^2-44 q+15+21 q^{-1} -28 q^{-2} +10 q^{-3} +9 q^{-4} -13 q^{-5} +5 q^{-6} +2 q^{-7} -3 q^{-8} + q^{-9} </math>|J3=<math>-q^{42}+2 q^{41}+q^{40}-2 q^{39}-6 q^{38}+4 q^{37}+11 q^{36}-21 q^{34}-5 q^{33}+26 q^{32}+21 q^{31}-34 q^{30}-34 q^{29}+29 q^{28}+55 q^{27}-23 q^{26}-70 q^{25}+8 q^{24}+83 q^{23}+9 q^{22}-90 q^{21}-28 q^{20}+90 q^{19}+51 q^{18}-91 q^{17}-63 q^{16}+75 q^{15}+87 q^{14}-71 q^{13}-92 q^{12}+44 q^{11}+112 q^{10}-35 q^9-107 q^8+9 q^7+112 q^6-96 q^4-14 q^3+87 q^2+11 q-65-10 q^{-1} +50 q^{-2} +2 q^{-3} -34 q^{-4} +3 q^{-5} +24 q^{-6} -9 q^{-7} -13 q^{-8} +8 q^{-9} +9 q^{-10} -9 q^{-11} -4 q^{-12} +6 q^{-13} + q^{-14} -2 q^{-15} -2 q^{-16} +3 q^{-17} - q^{-18} </math>|J4=<math>q^{70}-2 q^{69}-q^{68}+2 q^{67}+q^{66}+7 q^{65}-8 q^{64}-9 q^{63}+q^{61}+33 q^{60}-5 q^{59}-23 q^{58}-22 q^{57}-26 q^{56}+72 q^{55}+28 q^{54}-4 q^{53}-47 q^{52}-107 q^{51}+75 q^{50}+62 q^{49}+74 q^{48}-12 q^{47}-200 q^{46}+16 q^{45}+23 q^{44}+160 q^{43}+104 q^{42}-225 q^{41}-45 q^{40}-105 q^{39}+169 q^{38}+234 q^{37}-159 q^{36}-31 q^{35}-256 q^{34}+88 q^{33}+299 q^{32}-59 q^{31}+69 q^{30}-360 q^{29}-39 q^{28}+284 q^{27}+30 q^{26}+213 q^{25}-409 q^{24}-172 q^{23}+220 q^{22}+103 q^{21}+367 q^{20}-415 q^{19}-306 q^{18}+121 q^{17}+167 q^{16}+518 q^{15}-371 q^{14}-418 q^{13}-12 q^{12}+182 q^{11}+630 q^{10}-261 q^9-446 q^8-139 q^7+116 q^6+627 q^5-126 q^4-349 q^3-182 q^2+4 q+492-38 q^{-1} -195 q^{-2} -127 q^{-3} -68 q^{-4} +302 q^{-5} -22 q^{-6} -73 q^{-7} -42 q^{-8} -79 q^{-9} +151 q^{-10} -29 q^{-11} -14 q^{-12} +7 q^{-13} -56 q^{-14} +64 q^{-15} -26 q^{-16} +4 q^{-17} +16 q^{-18} -30 q^{-19} +23 q^{-20} -14 q^{-21} +4 q^{-22} +9 q^{-23} -11 q^{-24} +6 q^{-25} -4 q^{-26} +2 q^{-27} +2 q^{-28} -3 q^{-29} + q^{-30} </math>|J5=Not Available|J6=Not Available|J7=Not Available}}

{{Computer Talk Header}}

<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><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</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>PD[Knot[10, 28]]</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>PD[X[1, 4, 2, 5], X[3, 10, 4, 11], X[13, 19, 14, 18], X[5, 15, 6, 14], 
 
  X[17, 7, 18, 6], X[7, 17, 8, 16], X[15, 9, 16, 8], X[11, 1, 12, 20], 
 
  X[19, 13, 20, 12], X[9, 2, 10, 3]]</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>GaussCode[Knot[10, 28]]</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>GaussCode[-1, 10, -2, 1, -4, 5, -6, 7, -10, 2, -8, 9, -3, 4, -7, 6, -5, 
 
  3, -9, 8]</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>DTCode[Knot[10, 28]]</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>DTCode[4, 10, 14, 16, 2, 20, 18, 8, 6, 12]</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 = BR[Knot[10, 28]]</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[5, {1, 1, 2, -1, 2, 2, 3, -2, -4, 3, -4, -4}]</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>{First[br], Crossings[br]}</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>{5, 12}</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>BraidIndex[Knot[10, 28]]</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>5</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>Show[DrawMorseLink[Knot[10, 28]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_28_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</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[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 28]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</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>{Reversible, 2, 2, 2, NotAvailable, 1}</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>alex = Alexander[Knot[10, 28]][t]</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>     4    13             2
19 + -- - -- - 13 t + 4 t
      2   t
     t</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>Conway[Knot[10, 28]][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      4
1 + 3 z  + 4 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>Select[AllKnots[], (alex === Alexander[#][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>{Knot[10, 28], Knot[10, 37]}</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>{KnotDet[Knot[10, 28]], KnotSignature[Knot[10, 28]]}</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>{53, 0}</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>Jones[Knot[10, 28]][q]</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>     -3   3    5            2      3      4      5      6    7
7 - q   + -- - - - 8 q + 9 q  - 7 q  + 6 q  - 4 q  + 2 q  - q
           2   q
          q</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>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[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 28]}</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>A2Invariant[Knot[10, 28]][q]</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>      -10    -8    -6   2     -2      4    6      8    14      16    22
-1 - q    + q   + q   - -- + q   + 2 q  + q  + 3 q  + q   - 2 q   - q
                         4
                        q</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 28]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                 2    2      2                 4      4
      -6   3    z    z    4 z     2  2    4   z    2 z
-1 - a   + -- - -- + -- + ---- - a  z  + z  + -- + ----
            2    6    4     2                  4     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[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 28]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                      2       2
      -6   3    4 z   6 z   2 z   z            2   5 z    10 z
-1 + a   - -- - --- - --- - --- + - + a z + 4 z  - ---- + ----- - 
            2    7     5     3    a                  6      2
           a    a     a     a                       a      a
 
             3       3       3      3                               4
   2  2   8 z    18 z    13 z    2 z         3    3  3      4   12 z
  a  z  + ---- + ----- + ----- - ---- - 4 a z  + a  z  - 8 z  + ----- + 
            7      5       3      a                               6
           a      a       a                                      a
 
      4       4                5       5       5      5
  11 z    12 z       2  4   5 z    12 z    18 z    6 z         5
  ----- - ----- + 3 a  z  - ---- - ----- - ----- - ---- + 5 a z  + 
    4       2                 7      5       3      a
   a       a                 a      a       a
 
            6       6    6    7      7      7      8      8      8
     6   9 z    16 z    z    z    4 z    5 z    2 z    5 z    3 z
  6 z  - ---- - ----- - -- + -- + ---- + ---- + ---- + ---- + ---- + 
           6      4      2    7     3     a       6      4      2
          a      a      a    a     a             a      a      a
 
   9    9
  z    z
  -- + --
   5    3
  a    a</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 28]], Vassiliev[3][Knot[10, 28]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{3, 4}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 28]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4           1       2       1      3      2               3
- + 4 q + ----- + ----- + ----- + ---- + --- + 5 q t + 3 q  t + 
q          7  3    5  2    3  2    3     q t
          q  t    q  t    q  t    q  t
 
     3  2      5  2      5  3      7  3      7  4      9  4    9  5
  4 q  t  + 5 q  t  + 3 q  t  + 4 q  t  + 3 q  t  + 3 q  t  + q  t  + 
 
     11  5    11  6    13  6    15  7
  3 q   t  + q   t  + q   t  + q   t</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 28], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -9   3    2    5    13   9    10   28   21              2
15 + q   - -- + -- + -- - -- + -- + -- - -- + -- - 44 q + 29 q  + 
            8    7    6    5    4    3    2   q
           q    q    q    q    q    q    q
 
      3       4       5       6       7       8       9       10
  23 q  - 54 q  + 26 q  + 32 q  - 53 q  + 16 q  + 34 q  - 41 q   + 
 
     11       12       13      14       15      16      17      18
  4 q   + 29 q   - 24 q   - 4 q   + 18 q   - 9 q   - 5 q   + 7 q   - 
 
   19      20    21
  q   - 2 q   + q</nowiki></pre></td></tr>

</table>

See/edit the [[Rolfsen_Splice_Template]].

 [[Category:Knot Page]]