L11a365: Difference between revisions
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{{Link Page| |
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n = 11 | |
n = 11 | |
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t = |
t = a | |
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k = 365 | |
k = 365 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-5,6,-9,8,-10:5,-1,2,-3,11,-4,7,-6,9,-8,10,-7/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-5,6,-9,8,-10:5,-1,2,-3,11,-4,7,-6,9,-8,10,-7/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:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]</td></tr> |
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khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
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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> |
</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>11</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[11, Alternating, 365]]]</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 align=left> |
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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[12, 1, 13, 2], X[2, 13, 3, 14], X[14, 3, 15, 4], X[16, 5, 17, 6], |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>11</nowiki></code></td></tr> |
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<table><tr align=left> |
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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[11, Alternating, 365]]]</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[12, 1, 13, 2], X[2, 13, 3, 14], X[14, 3, 15, 4], X[16, 5, 17, 6], |
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X[6, 11, 7, 12], X[18, 8, 19, 7], X[22, 18, 11, 17], |
X[6, 11, 7, 12], X[18, 8, 19, 7], X[22, 18, 11, 17], |
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X[20, 10, 21, 9], X[8, 20, 9, 19], X[10, 22, 1, 21], X[4, 15, 5, 16]]</nowiki></ |
X[20, 10, 21, 9], X[8, 20, 9, 19], X[10, 22, 1, 21], X[4, 15, 5, 16]]</nowiki></pre></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[5]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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{5, -1, 2, -3, 11, -4, 7, -6, 9, -8, 10, -7}]</nowiki></ |
{5, -1, 2, -3, 11, -4, 7, -6, 9, -8, 10, -7}]</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[3, {1, 1, 1, -2, -2, -2, -2, -2, 1, -2, 1}]</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[11, Alternating, 365]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a365_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[11, Alternating, 365]]</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:L11a365_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[11, Alternating, 365]][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 3 5 7 7 8 |
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</table> |
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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[11, Alternating, 365]]</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 3 5 7 7 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 7/2 9/2 |
3/2 5/2 7/2 9/2 |
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5 q + 3 q - 2 q + q</nowiki></ |
5 q + 3 q - 2 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 + q + -- + q + q + q - q - q |
3 + q + q - q + q + -- + q + q + q - q - q |
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4 |
4 |
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q</nowiki></ |
q</nowiki></pre></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[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 6 z 3 11 z 3 3 3 6 z |
a a 6 z 3 11 z 3 3 3 6 z |
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-(-) + -- + --- - 13 a z + 6 a z + ----- - 28 a z + 11 a z + ---- - |
-(-) + -- + --- - 13 a z + 6 a z + ----- - 28 a z + 11 a z + ---- - |
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5 3 5 z 7 3 7 9 |
5 3 5 z 7 3 7 9 |
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23 a z + 6 a z + -- - 8 a z + a z - a z |
23 a z + 6 a z + -- - 8 a z + a z - a z |
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a</nowiki></ |
a</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[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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2 a a z 6 z 3 7 2 3 z z |
2 a a z 6 z 3 7 2 3 z z |
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-a + - + -- + -- - --- - 14 a z - 6 a z - a z + 6 z - ---- + -- + |
-a + - + -- + -- - --- - 14 a z - 6 a z - a z + 6 z - ---- + -- + |
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3 9 10 2 10 |
3 9 10 2 10 |
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2 a z - z - a z</nowiki></ |
2 a z - 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[11, Alternating, 365]][q, t]</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[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 5 10 5 10 4 8 4 8 3 6 3 |
2 14 6 12 5 10 5 10 4 8 4 8 3 6 3 |
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4 3 6 3 6 4 8 4 10 5 |
4 3 6 3 6 4 8 4 10 5 |
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q t + 2 q t + q t + q t + q t</nowiki></ |
q t + 2 q t + q t + q t + q t</nowiki></pre></td></tr> |
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</table> }} |
</table> }} |
Revision as of 18:58, 2 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a365's Link Presentations]
Planar diagram presentation | X12,1,13,2 X2,13,3,14 X14,3,15,4 X16,5,17,6 X6,11,7,12 X18,8,19,7 X22,18,11,17 X20,10,21,9 X8,20,9,19 X10,22,1,21 X4,15,5,16 |
Gauss code | {1, -2, 3, -11, 4, -5, 6, -9, 8, -10}, {5, -1, 2, -3, 11, -4, 7, -6, 9, -8, 10, -7} |
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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