L10a148: Difference between revisions
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n = 10 | |
n = 10 | |
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t = |
t = a | |
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k = 148 | |
k = 148 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10:3,-1,6,-5,7,-8,9,-4:8,-2,4,-3,10,-6,5,-7/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10:3,-1,6,-5,7,-8,9,-4:8,-2,4,-3,10,-6,5,-7/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"> |
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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr> |
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<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> |
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<tr valign=top><td colspan=2 |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</td></tr> |
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<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> |
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<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[10, Alternating, 148]]]</nowiki></pre></td></tr> |
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<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>3</nowiki></pre></td></tr> |
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<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[14, 4, 15, 3], X[16, 5, 17, 6], X[12, 15, 5, 16], |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>10</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Length[Skeleton[Link[10, Alternating, 148]]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>3</nowiki></code></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
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<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[14, 4, 15, 3], X[16, 5, 17, 6], X[12, 15, 5, 16], |
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X[8, 20, 9, 19], X[18, 8, 19, 7], X[20, 10, 13, 9], |
X[8, 20, 9, 19], X[18, 8, 19, 7], X[20, 10, 13, 9], |
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X[10, 14, 11, 13], X[2, 11, 3, 12], X[4, 18, 1, 17]]</nowiki></ |
X[10, 14, 11, 13], X[2, 11, 3, 12], X[4, 18, 1, 17]]</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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{8, -2, 4, -3, 10, -6, 5, -7}]</nowiki></ |
{8, -2, 4, -3, 10, -6, 5, -7}]</nowiki></pre></td></tr> |
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<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, 1, 1, 1, 1, -2, 1, -2, -2}]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<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[10, Alternating, 148]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L10a148_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> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
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<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[10, Alternating, 148]]</nowiki></pre></td></tr> |
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<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>2</nowiki></pre></td></tr> |
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<tr align=left><td></td><td>[[Image:L10a148_ML.gif]]</td></tr><tr align=left> |
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< |
<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[10, Alternating, 148]][q]</nowiki></pre></td></tr> |
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<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> -3 3 5 2 3 4 5 6 7 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>KnotSignature[Link[10, Alternating, 148]]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>2</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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-6 + q - -- + - + 10 q - 9 q + 10 q - 7 q + 5 q - 3 q + q |
-6 + q - -- + - + 10 q - 9 q + 10 q - 7 q + 5 q - 3 q + q |
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2 q |
2 q |
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q</nowiki></ |
q</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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2 + q - q + q + 5 q + 3 q + 8 q + 3 q + 4 q + q - q + |
2 + q - q + q + 5 q + 3 q + 8 q + 3 q + 4 q + q - q + |
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16 18 20 |
16 18 20 |
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q - q + q</nowiki></ |
q - q + q</nowiki></pre></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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-4 3 -2 1 2 2 4 z 9 z 4 4 z |
-4 3 -2 1 2 2 4 z 9 z 4 4 z |
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2 + a - -- + z + ----- - ----- + 4 z + ---- - ---- + 4 z + ---- - |
2 + a - -- + z + ----- - ----- + 4 z + ---- - ---- + 4 z + ---- - |
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----- + z + -- - ---- - -- |
----- + z + -- - ---- - -- |
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2 4 2 2 |
2 4 2 2 |
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a a a a</nowiki></ |
a a a a</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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3 + -- + -- - z - ----- - ----- + ---- + --- - --- - --- - 9 z - |
3 + -- + -- - z - ----- - ----- + ---- + --- - --- - --- - 9 z - |
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4 2 4 2 2 2 3 a z 3 a |
4 2 4 2 2 2 3 a z 3 a |
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---- - ---- + 3 a z + 4 z + ---- + ---- + ---- + ---- |
---- - ---- + 3 a z + 4 z + ---- + ---- + ---- + ---- |
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3 a 4 2 3 a |
3 a 4 2 3 a |
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a a a a</nowiki></ |
a a a a</nowiki></pre></td></tr> |
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<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[10, Alternating, 148]][q, t]</nowiki></pre></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 2 1 3 2 3 3 q |
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7 q + 6 q + ----- + ----- + ----- + ----- + ---- + --- + --- + |
7 q + 6 q + ----- + ----- + ----- + ----- + ---- + --- + --- + |
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7 4 5 3 3 3 3 2 2 q t t |
7 4 5 3 3 3 3 2 2 q t t |
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11 4 11 5 13 5 15 6 |
11 4 11 5 13 5 15 6 |
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3 q t + q t + 2 q t + q t</nowiki></ |
3 q t + q t + 2 q t + q t</nowiki></pre></td></tr> |
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</table> }} |
</table> }} |
Latest revision as of 03:49, 3 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10a148's Link Presentations]
Planar diagram presentation | X6172 X14,4,15,3 X16,5,17,6 X12,15,5,16 X8,20,9,19 X18,8,19,7 X20,10,13,9 X10,14,11,13 X2,11,3,12 X4,18,1,17 |
Gauss code | {1, -9, 2, -10}, {3, -1, 6, -5, 7, -8, 9, -4}, {8, -2, 4, -3, 10, -6, 5, -7} |
A Braid Representative | ||||
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 2 (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 ). |
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Integral Khovanov Homology
(db, data source) |
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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. |
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