L9a33: Difference between revisions
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{{Link Page| |
{{Link Page| |
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n = 9 | |
n = 9 | |
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t = |
t = a | |
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k = 33 | |
k = 33 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-7,2,-8,5,-9:7,-1,3,-4,8,-2,4,-6,9,-5,6,-3/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-7,2,-8,5,-9:7,-1,3,-4,8,-2,4,-6,9,-5,6,-3/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0> |
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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
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<tr align=center> |
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<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
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</tr> |
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<tr valign=top><td colspan=2 |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</td></tr> |
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</table> |
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<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>9</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<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[9, Alternating, 33]]]</nowiki></pre></td></tr> |
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<td>< |
<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>2</nowiki></pre></td></tr> |
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<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>PD[X[8, 1, 9, 2], X[12, 3, 13, 4], X[18, 10, 7, 9], X[10, 14, 11, 13], |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>9</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Length[Skeleton[Link[9, Alternating, 33]]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>2</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[8, 1, 9, 2], X[12, 3, 13, 4], X[18, 10, 7, 9], X[10, 14, 11, 13], |
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X[16, 5, 17, 6], X[14, 18, 15, 17], X[2, 7, 3, 8], X[4, 11, 5, 12], |
X[16, 5, 17, 6], X[14, 18, 15, 17], X[2, 7, 3, 8], X[4, 11, 5, 12], |
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X[6, 15, 1, 16]]</nowiki></ |
X[6, 15, 1, 16]]</nowiki></pre></td></tr> |
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</table> |
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<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>GaussCode[{1, -7, 2, -8, 5, -9}, |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[{1, -7, 2, -8, 5, -9}, |
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{7, -1, 3, -4, 8, -2, 4, -6, 9, -5, 6, -3}]</nowiki></ |
{7, -1, 3, -4, 8, -2, 4, -6, 9, -5, 6, -3}]</nowiki></pre></td></tr> |
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</table> |
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<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>BR[5, {1, -2, -3, -2, 1, -2, -4, 3, -2, 1, -2, -3, 4, 3, -2}]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<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[9, Alternating, 33]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L9a33_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> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
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<td>< |
<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[9, Alternating, 33]]</nowiki></pre></td></tr> |
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<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>-1</nowiki></pre></td></tr> |
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<tr align=left><td></td><td>[[Image:L9a33_ML.gif]]</td></tr><tr align=left> |
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< |
<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[9, Alternating, 33]][q]</nowiki></pre></td></tr> |
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<td>< |
<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> -(13/2) 2 6 7 9 10 8 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>KnotSignature[Link[9, Alternating, 33]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-1</nowiki></code></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -(13/2) 2 6 7 9 10 8 |
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-q + ----- - ---- + ---- - ---- + ---- - ------- + 6 Sqrt[q] - |
-q + ----- - ---- + ---- - ---- + ---- - ------- + 6 Sqrt[q] - |
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11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
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3/2 5/2 |
3/2 5/2 |
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4 q + q</nowiki></ |
4 q + q</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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3 + q + --- + --- + --- + --- - q - -- - -- - q + 2 q - q |
3 + q + --- + --- + --- + --- - q - -- - -- - q + 2 q - q |
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20 16 14 10 6 2 |
20 16 14 10 6 2 |
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q q q q q q</nowiki></ |
q q q q q q</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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a a 3 5 z 3 3 3 5 |
a a 3 5 z 3 3 3 5 |
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-(--) + -- - 3 a z + 3 a z - 3 a z + -- - 2 a z + 3 a z - a z |
-(--) + -- - 3 a z + 3 a z - 3 a z + -- - 2 a z + 3 a z - a z |
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z z a</nowiki></ |
z z a</nowiki></pre></td></tr> |
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</table> |
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<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> 5 7 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 5 7 |
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6 a a 3 5 7 2 2 2 |
6 a a 3 5 7 2 2 2 |
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-a + -- + -- - 2 a z + 2 a z + a z - 3 a z - 3 z - 14 a z - |
-a + -- + -- - 2 a z + 2 a z + a z - 3 a z - 3 z - 14 a z - |
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5 7 2 8 4 8 |
5 7 2 8 4 8 |
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3 a z - a z - a z</nowiki></ |
3 a z - a z - a z</nowiki></pre></td></tr> |
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<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[9, Alternating, 33]][q, t]</nowiki></pre></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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5 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
5 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
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2 14 6 12 6 12 5 10 4 8 4 8 3 6 3 |
2 14 6 12 6 12 5 10 4 8 4 8 3 6 3 |
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----- + ----- + ---- + ---- + 3 t + 3 q t + q t + 3 q t + q t |
----- + ----- + ---- + ---- + 3 t + 3 q t + q t + 3 q t + q t |
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6 2 4 2 4 2 |
6 2 4 2 4 2 |
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q t q t q t q t</nowiki></ |
q t q t q t q t</nowiki></pre></td></tr> |
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</table> }} |
</table> }} |
Revision as of 19:07, 2 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
L9a33 is in the Rolfsen table of links. |
Link Presentations
[edit Notes on L9a33's Link Presentations]
Planar diagram presentation | X8192 X12,3,13,4 X18,10,7,9 X10,14,11,13 X16,5,17,6 X14,18,15,17 X2738 X4,11,5,12 X6,15,1,16 |
Gauss code | {1, -7, 2, -8, 5, -9}, {7, -1, 3, -4, 8, -2, 4, -6, 9, -5, 6, -3} |
A Braid Representative | ||||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -1 (db) |
HOMFLY-PT polynomial | (db) |
Kauffman polynomial | (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). |
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Integral Khovanov Homology
(db, data source) |
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Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. |
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