L11n86: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
(One intermediate revision by the same user not shown) | |||
Line 1: | Line 1: | ||
<!-- WARNING! WARNING! WARNING! |
<!-- WARNING! WARNING! WARNING! |
||
<!-- This page was generated from the splice |
<!-- This page was generated from the splice template [[Link_Splice_Base]]. Please do not edit! |
||
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].) |
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].) |
||
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link_Splice_Base]]. --> |
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link_Splice_Base]]. --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
<!-- WARNING! WARNING! WARNING! |
<!-- WARNING! WARNING! WARNING! |
||
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit! |
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit! |
||
Line 10: | Line 10: | ||
<!-- The text below simply calls [[Template:Link Page]] setting the values of all the parameters appropriately. |
<!-- The text below simply calls [[Template:Link Page]] setting the values of all the parameters appropriately. |
||
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link Splice Template]]. --> |
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link Splice Template]]. --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
{{Link Page| |
{{Link Page| |
||
n = 11 | |
n = 11 | |
||
t = |
t = n | |
||
k = 86 | |
k = 86 | |
||
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,3,-8,4,-9,11,-2,9,-3,-6,7,8,-4,-5,6,-7,5/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:10,-1,3,-8,4,-9,11,-2,9,-3,-6,7,8,-4,-5,6,-7,5/goTop.html | |
||
braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"> |
|||
<tr><td>[[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:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.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:BraidPart1.gif]][[Image:BraidPart1.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
⚫ | |||
khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
||
<tr align=center> |
<tr align=center> |
||
Line 42: | Line 49: | ||
<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> |
||
</tr> |
</tr> |
||
<tr valign=top><td colspan=2 |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</td></tr> |
||
⚫ | |||
</table> |
|||
<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> |
|||
<table><tr align=left> |
|||
< |
<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, NonAlternating, 86]]]</nowiki></pre></td></tr> |
||
<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> |
||
⚫ | |||
<tr align=left> |
|||
< |
<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[6, 1, 7, 2], X[12, 3, 13, 4], X[14, 8, 15, 7], X[18, 10, 19, 9], |
||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>11</nowiki></code></td></tr> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Length[Skeleton[Link[11, NonAlternating, 86]]]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>2</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[14, 8, 15, 7], X[18, 10, 19, 9], |
|||
X[19, 5, 20, 22], X[15, 21, 16, 20], X[21, 17, 22, 16], |
X[19, 5, 20, 22], X[15, 21, 16, 20], X[21, 17, 22, 16], |
||
X[8, 18, 9, 17], X[10, 14, 11, 13], X[2, 5, 3, 6], X[4, 11, 1, 12]]</nowiki></ |
X[8, 18, 9, 17], X[10, 14, 11, 13], X[2, 5, 3, 6], X[4, 11, 1, 12]]</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
|||
⚫ | |||
7, 8, -4, -5, 6, -7, 5}]</nowiki></ |
7, 8, -4, -5, 6, -7, 5}]</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
<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, 1, 2, 3, -2, 4, -3, -2, 1, -2, 3, -2, 1, -4, -3, 2, 2}]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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, NonAlternating, 86]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n86_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> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
|||
<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, NonAlternating, 86]]</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>3</nowiki></pre></td></tr> |
|||
<tr align=left><td></td><td>[[Image:L11n86_ML.gif]]</td></tr><tr align=left> |
|||
< |
<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, NonAlternating, 86]][q]</nowiki></pre></td></tr> |
||
<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> -(5/2) -(3/2) 4 3/2 5/2 7/2 |
||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>KnotSignature[Link[11, NonAlternating, 86]]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>3</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -(5/2) -(3/2) 4 3/2 5/2 7/2 |
|||
-q + q - ------- + 4 Sqrt[q] - 6 q + 6 q - 5 q + |
-q + q - ------- + 4 Sqrt[q] - 6 q + 6 q - 5 q + |
||
Sqrt[q] |
Sqrt[q] |
||
9/2 11/2 13/2 |
9/2 11/2 13/2 |
||
5 q - 3 q + q</nowiki></ |
5 q - 3 q + q</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
|||
⚫ | |||
3 + q + -- + -- + -- + 3 q + q - q - 4 q - q - 2 q + q + |
3 + q + -- + -- + -- + 3 q + q - q - 4 q - q - 2 q + q + |
||
6 4 2 |
6 4 2 |
||
Line 115: | Line 83: | ||
22 24 |
22 24 |
||
q - q</nowiki></ |
q - q</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
|||
⚫ | |||
2 5 3 a z 3 z 7 z 11 z 4 z 8 z 9 z |
2 5 3 a z 3 z 7 z 11 z 4 z 8 z 9 z |
||
---- - --- + --- + -- - --- + --- - ---- + 4 a z - ---- + ---- - ---- + |
---- - --- + --- + -- - --- + --- - ---- + 4 a z - ---- + ---- - ---- + |
||
Line 132: | Line 95: | ||
a z - -- + ---- - ---- + -- |
a z - -- + ---- - ---- + -- |
||
5 3 a 3 |
5 3 a 3 |
||
a a a</nowiki></ |
a a a</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
|||
⚫ | |||
5 - a + -- - ---- - --- - --- + -- + --- + --- + ---- + 10 a z - |
5 - a + -- - ---- - --- - --- + -- + --- + --- + ---- + 10 a z - |
||
2 3 a z z 7 5 3 a |
2 3 a z z 7 5 3 a |
||
Line 166: | Line 124: | ||
-- - -- |
-- - -- |
||
3 a |
3 a |
||
a</nowiki></ |
a</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>Kh[Link[11, NonAlternating, 86]][q, t]</nowiki></pre></td></tr> |
|||
</table> |
|||
⚫ | |||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
|||
⚫ | |||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
|||
⚫ | |||
2 4 1 1 1 -2 3 1 3 q 4 |
2 4 1 1 1 -2 3 1 3 q 4 |
||
5 q + 2 q + ----- + ----- + ----- + t + ----- + - + ---- + 2 q t + |
5 q + 2 q + ----- + ----- + ----- + t + ----- + - + ---- + 2 q t + |
||
Line 183: | Line 136: | ||
14 5 |
14 5 |
||
q t</nowiki></ |
q t</nowiki></pre></td></tr> |
||
</table> }} |
</table> }} |
Latest revision as of 02:21, 3 September 2005
|
|
(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11n86's Link Presentations]
Planar diagram presentation | X6172 X12,3,13,4 X14,8,15,7 X18,10,19,9 X19,5,20,22 X15,21,16,20 X21,17,22,16 X8,18,9,17 X10,14,11,13 X2536 X4,11,1,12 |
Gauss code | {1, -10, 2, -11}, {10, -1, 3, -8, 4, -9, 11, -2, 9, -3, -6, 7, 8, -4, -5, 6, -7, 5} |
A Braid Representative | ||||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 3 (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 ). |
|
Integral Khovanov Homology
(db, data source) |
|
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. |
|