10 48: 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 49: | Line 52: | ||
<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, 48]]</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, 48]]</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[6, 2, 7, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[20, 15, 1, 16], |
<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[6, 2, 7, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[20, 15, 1, 16], |
||
Line 69: | Line 72: | ||
<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>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>Show[DrawMorseLink[Knot[10, 48]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_48_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, 48]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_48_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, 48]]&) /@ { |
<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, 48]]&) /@ { |
||
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, 4, 3, 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, 4, 3, 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, 48]][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, 48]][t]</nowiki></pre></td></tr> |
Revision as of 17:42, 31 August 2005
|
|
![]() (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 48's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X8493 X14,6,15,5 X20,15,1,16 X16,9,17,10 X18,11,19,12 X10,17,11,18 X12,19,13,20 X2837 X4,14,5,13 |
Gauss code | 1, -9, 2, -10, 3, -1, 9, -2, 5, -7, 6, -8, 10, -3, 4, -5, 7, -6, 8, -4 |
Dowker-Thistlethwaite code | 6 8 14 2 16 18 4 20 10 12 |
Conway Notation | [41,3,2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||
Length is 10, width is 3, Braid index is 3 |
![]() |
![]() [{5, 13}, {2, 12}, {13, 11}, {12, 6}, {1, 4}, {3, 5}, {4, 7}, {6, 8}, {7, 9}, {8, 10}, {9, 3}, {11, 2}, {10, 1}] |
[edit Notes on presentations of 10 48]
Three dimensional invariants
|
Four dimensional invariants
|
Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (4, 0) |
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 0 is the signature of 10 48. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
Integral Khovanov Homology
(db, data source) |
|