L11a164: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
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 = a | |
||
k = 164 | |
k = 164 | |
||
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-10:10,-1,2,-3,6,-7,11,-4,5,-9,8,-6,7,-5,9,-8/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-10:10,-1,2,-3,6,-7,11,-4,5,-9,8,-6,7,-5,9,-8/goTop.html | |
||
braid_table = <table cellspacing=0 cellpadding=0 border=0> |
|||
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
⚫ | |||
khovanov_table = <table border=1> |
khovanov_table = <table border=1> |
||
<tr align=center> |
<tr align=center> |
||
Line 44: | 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 2, 2005, 15:8:39)...</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, Alternating, 164]]]</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[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[14, 5, 15, 6], |
||
<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, Alternating, 164]]]</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[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[14, 5, 15, 6], |
|||
X[20, 16, 21, 15], X[18, 12, 19, 11], X[12, 20, 13, 19], |
X[20, 16, 21, 15], X[18, 12, 19, 11], X[12, 20, 13, 19], |
||
X[22, 18, 7, 17], X[16, 22, 17, 21], X[6, 7, 1, 8], X[4, 13, 5, 14]]</nowiki></ |
X[22, 18, 7, 17], X[16, 22, 17, 21], X[6, 7, 1, 8], X[4, 13, 5, 14]]</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> |
|||
⚫ | |||
{10, -1, 2, -3, 6, -7, 11, -4, 5, -9, 8, -6, 7, -5, 9, -8}]</nowiki></ |
{10, -1, 2, -3, 6, -7, 11, -4, 5, -9, 8, -6, 7, -5, 9, -8}]</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[3, {1, -2, -2, 1, 1, 1, -2, -2, -2, -2, 1}]</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, Alternating, 164]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a164_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, Alternating, 164]]</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>-1</nowiki></pre></td></tr> |
|||
<tr align=left><td></td><td>[[Image:L11a164_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, Alternating, 164]][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> -(13/2) 2 5 8 11 12 13 |
||
</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, Alternating, 164]]</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>-1</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> -(13/2) 2 5 8 11 12 13 |
|||
-q + ----- - ---- + ---- - ---- + ---- - ------- + 10 Sqrt[q] - |
-q + ----- - ---- + ---- - ---- + ---- - ------- + 10 Sqrt[q] - |
||
11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
11/2 9/2 7/2 5/2 3/2 Sqrt[q] |
||
Line 105: | Line 76: | ||
3/2 5/2 7/2 9/2 |
3/2 5/2 7/2 9/2 |
||
8 q + 5 q - 2 q + q</nowiki></ |
8 q + 5 q - 2 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> |
|||
⚫ | |||
4 + q + --- + --- + -- - q + -- - q - q - 3 q - q |
4 + q + --- + --- + -- - q + -- - q - q - 3 q - q |
||
14 10 8 4 |
14 10 8 4 |
||
q q q q</nowiki></ |
q q 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 a 3 a 11 z 3 13 z 3 |
2 5 a 3 a 11 z 3 13 z 3 |
||
--- - --- + ---- + ---- - 25 a z + 11 a z + ----- - 37 a z + |
--- - --- + ---- + ---- - 25 a z + 11 a z + ----- - 37 a z + |
||
Line 130: | Line 91: | ||
3 3 6 z 5 3 5 z 7 3 7 9 |
3 3 6 z 5 3 5 z 7 3 7 9 |
||
13 a z + ---- - 25 a z + 6 a z + -- - 8 a z + a z - a z |
13 a z + ---- - 25 a z + 6 a z + -- - 8 a z + a z - a z |
||
a a</nowiki></ |
a a</nowiki></pre></td></tr> |
||
⚫ | |||
</table> |
|||
<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> 3 |
|||
<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> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 |
|||
-4 2 2 5 a 3 a 11 z 3 5 |
-4 2 2 5 a 3 a 11 z 3 5 |
||
-5 + a - 5 a + --- + --- + ---- - ---- - 28 a z - 13 a z + 2 a z - |
-5 + a - 5 a + --- + --- + ---- - ---- - 28 a z - 13 a z + 2 a z - |
||
Line 175: | Line 131: | ||
2 8 4 8 3 z 9 3 9 10 2 10 |
2 8 4 8 3 z 9 3 9 10 2 10 |
||
3 a z - 3 a z - ---- - 6 a z - 3 a z - z - a z |
3 a z - 3 a z - ---- - 6 a z - 3 a z - z - a z |
||
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, Alternating, 164]][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> |
|||
⚫ | |||
7 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
7 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
||
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 |
||
Line 193: | Line 144: | ||
4 3 6 3 6 4 8 4 10 5 |
4 3 6 3 6 4 8 4 10 5 |
||
q t + 4 q t + q t + q t + q t</nowiki></ |
q t + 4 q t + q t + q t + q t</nowiki></pre></td></tr> |
||
</table> }} |
</table> }} |
Revision as of 18:12, 2 September 2005
|
|
(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L11a164's Link Presentations]
Planar diagram presentation | X8192 X2,9,3,10 X10,3,11,4 X14,5,15,6 X20,16,21,15 X18,12,19,11 X12,20,13,19 X22,18,7,17 X16,22,17,21 X6718 X4,13,5,14 |
Gauss code | {1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, 6, -7, 11, -4, 5, -9, 8, -6, 7, -5, 9, -8} |
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 ). |
|
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. |
|