L10a23: 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! |
|||
<!-- This page was |
<!-- 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]].) |
|||
--> |
|||
<!-- 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! |
|||
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit! |
|||
<!-- Almost certainly, you want to edit [[Template:Link Page]], which actually produces this page. |
|||
<!-- 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]]. --> |
|||
<!-- <math>\text{Null}</math> --> |
|||
{{Link Page| |
{{Link Page| |
||
n = 10 | |
n = 10 | |
||
Line 34: | Line 43: | ||
<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>Loading KnotTheory` (version of August |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 28, 2005, 22:58:49)...</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>Crossings[Link[10, Alternating, 23]]</nowiki></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>Crossings[Link[10, Alternating, 23]]</nowiki></pre></td></tr> |
||
<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>10</nowiki></pre></td></tr> |
<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>10</nowiki></pre></td></tr> |
||
Line 49: | Line 58: | ||
4, -3, 5, -9}]</nowiki></pre></td></tr> |
4, -3, 5, -9}]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: |
<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>Show[DrawMorseLink[Link[10, Alternating, 23]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L10a23_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[6]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
||
<tr valign=top><td><pre |
<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>KnotSignature[Link[10, Alternating, 23]]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>-3</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> |
<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>J=Jones[Link[10, Alternating, 23]][q]</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> |
<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> -(17/2) 3 7 10 12 14 12 10 |
||
<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>Conway[Link[10, Alternating, 23]][z]</nowiki></pre></td></tr> |
|||
<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>ComplexInfinity</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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</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>{KnotDet[Link[10, Alternating, 23]], KnotSignature[Link[10, Alternating, 23]]}</nowiki></pre></td></tr> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Infinity, -3}</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>J=Jones[Link[10, Alternating, 23]][q]</nowiki></pre></td></tr> |
|||
<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> -(17/2) 3 7 10 12 14 12 10 |
|||
q - ----- + ----- - ----- + ---- - ---- + ---- - ---- + |
q - ----- + ----- - ----- + ---- - ---- + ---- - ---- + |
||
15/2 13/2 11/2 9/2 7/2 5/2 3/2 |
15/2 13/2 11/2 9/2 7/2 5/2 3/2 |
||
Line 69: | Line 70: | ||
------- - 4 Sqrt[q] + q |
------- - 4 Sqrt[q] + q |
||
Sqrt[q]</nowiki></pre></td></tr> |
Sqrt[q]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<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>A2Invariant[Link[10, Alternating, 23]][q]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<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> -26 3 -18 2 -14 3 5 -6 3 2 2 4 |
||
-q - --- + q - --- + q + --- + -- - q + -- + -- + 2 q - q |
-q - --- + q - --- + q + --- + -- - q + -- + -- + 2 q - q |
||
20 16 12 8 4 2 |
20 16 12 8 4 2 |
||
q q q q q q</nowiki></pre></td></tr> |
q q q q q q</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<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>HOMFLYPT[Link[10, Alternating, 23]][a, z]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 5 7 |
||
a 2 a a 3 5 7 3 3 3 |
a 2 a a 3 5 7 3 3 3 |
||
-(-) + ---- - -- - a z - 2 a z + 5 a z - 2 a z + 2 a z - 5 a z + |
-(-) + ---- - -- - a z - 2 a z + 5 a z - 2 a z + 2 a z - 5 a z + |
||
Line 82: | Line 83: | ||
5 3 7 3 5 3 5 5 5 3 7 |
5 3 7 3 5 3 5 5 5 3 7 |
||
6 a z - a z + a z - 4 a z + 2 a z - a z</nowiki></pre></td></tr> |
6 a z - a z + a z - 4 a z + 2 a z - a z</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<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>Kauffman[Link[10, Alternating, 23]][a, z]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 5 7 |
||
2 4 6 8 a 2 a a 3 5 |
2 4 6 8 a 2 a a 3 5 |
||
-a + 3 a + 5 a + 2 a + - - ---- - -- - a z + 4 a z + 9 a z + |
-a + 3 a + 5 a + 2 a + - - ---- - -- - a z + 4 a z + 9 a z + |
||
Line 105: | Line 106: | ||
6 8 3 9 5 9 |
6 8 3 9 5 9 |
||
5 a z - 2 a z - 2 a z</nowiki></pre></td></tr> |
5 a z - 2 a z - 2 a z</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[ |
<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>Kh[Link[10, Alternating, 23]][q, t]</nowiki></pre></td></tr> |
||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[ |
<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 1 2 1 5 2 5 |
||
<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>Kh[Link[10, Alternating, 23]][q, t]</nowiki></pre></td></tr> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>5 7 1 2 1 5 2 5 |
|||
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
||
4 2 18 7 16 6 14 6 14 5 12 5 12 4 |
4 2 18 7 16 6 14 6 14 5 12 5 12 4 |
Revision as of 12:08, 31 August 2005
|
|
(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10a23's Link Presentations]
Planar diagram presentation | X6172 X16,7,17,8 X18,9,19,10 X8,17,9,18 X4,19,1,20 X14,12,15,11 X10,4,11,3 X12,5,13,6 X20,13,5,14 X2,16,3,15 |
Gauss code | {1, -10, 7, -5}, {8, -1, 2, -4, 3, -7, 6, -8, 9, -6, 10, -2, 4, -3, 5, -9} |
A Braid Representative | {{{braid_table}}} |
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. |
|