10 41: 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 [[Rolfsen_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 [[Rolfsen_Splice_Base]]. --> |
|||
<!-- <math>\text{Null}</math> --> |
|||
<!-- <math>\text{Null}</math> --> |
|||
{{Rolfsen Knot Page| |
{{Rolfsen Knot Page| |
||
n = 10 | |
n = 10 | |
||
Line 51: | Line 54: | ||
<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 29, 2005, 15: |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</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>PD[Knot[10, 41]]</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>PD[Knot[10, 41]]</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>PD[X[1, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], |
<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>PD[X[1, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], |
||
Line 71: | Line 74: | ||
<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>5</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>5</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>Show[DrawMorseLink[Knot[10, 41]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_41_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></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>Show[DrawMorseLink[Knot[10, 41]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_41_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
||
<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>(#[Knot[10, 41]]&) /@ { |
<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> (#[Knot[10, 41]]&) /@ { |
||
SymmetryType, UnknottingNumber, ThreeGenus, |
|||
BridgeIndex, SuperBridgeIndex, NakanishiIndex |
|||
}</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>{Reversible, 2, 3, 2, NotAvailable, 1}</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>{Reversible, 2, 3, 2, NotAvailable, 1}</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>alex = Alexander[Knot[10, 41]][t]</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>alex = Alexander[Knot[10, 41]][t]</nowiki></pre></td></tr> |
Revision as of 18:48, 31 August 2005
|
|
![]() (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 41's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X9,20,10,1 X15,19,16,18 X13,8,14,9 X17,6,18,7 X7,16,8,17 X19,15,20,14 |
Gauss code | -1, 4, -3, 1, -2, 8, -9, 7, -5, 3, -4, 2, -7, 10, -6, 9, -8, 6, -10, 5 |
Dowker-Thistlethwaite code | 4 10 12 16 20 2 8 18 6 14 |
Conway Notation | [221212] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 |
![]() |
![]() [{12, 7}, {1, 10}, {11, 8}, {7, 9}, {10, 12}, {6, 11}, {8, 2}, {3, 1}, {2, 5}, {4, 6}, {5, 3}, {9, 4}] |
[edit Notes on presentations of 10 41]
Three dimensional invariants
|
Four dimensional invariants
|
Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11n5,}
Same Jones Polynomial (up to mirroring, ): {10_94,}
Vassiliev invariants
V2 and V3: | (-2, 2) |
V2,1 through V6,9: |
|
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where -2 is the signature of 10 41. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
Integral Khovanov Homology
(db, data source) |
|