10 107
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 107's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
| Planar diagram presentation | X1425 X3,12,4,13 X7,14,8,15 X9,19,10,18 X19,7,20,6 X5,17,6,16 X17,11,18,10 X13,8,14,9 X15,1,16,20 X11,2,12,3 |
| Gauss code | -1, 10, -2, 1, -6, 5, -3, 8, -4, 7, -10, 2, -8, 3, -9, 6, -7, 4, -5, 9 |
| Dowker-Thistlethwaite code | 4 12 16 14 18 2 8 20 10 6 |
| Conway Notation | [210:2:20] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 |
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 [{12, 2}, {1, 10}, {6, 11}, {10, 12}, {3, 7}, {2, 5}, {9, 6}, {7, 4}, {11, 8}, {5, 9}, {8, 3}, {4, 1}] |
[edit Notes on presentations of 10 107]
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 107"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1425 X3,12,4,13 X7,14,8,15 X9,19,10,18 X19,7,20,6 X5,17,6,16 X17,11,18,10 X13,8,14,9 X15,1,16,20 X11,2,12,3 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 10, -2, 1, -6, 5, -3, 8, -4, 7, -10, 2, -8, 3, -9, 6, -7, 4, -5, 9 |
In[6]:=
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DTCode[K]
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Out[6]=
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4 12 16 14 18 2 8 20 10 6 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
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ConwayNotation[K]
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Out[8]=
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[210:2:20] |
In[9]:=
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br = BR[K]
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KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
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Out[9]=
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[math]\displaystyle{ \textrm{BR}(5,\{-1,-1,2,-1,3,2,2,-4,3,-2,3,-4\}) }[/math] |
In[10]:=
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{First[br], Crossings[br], BraidIndex[K]}
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KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
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KnotTheory::loading: Loading precomputed data in IndianaData`.
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Out[10]=
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{ 5, 12, 5 } |
In[11]:=
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Show[BraidPlot[br]]
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Out[11]=
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-Graphics- |
In[12]:=
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Show[DrawMorseLink[K]]
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KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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Out[12]=
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-Graphics- |
In[13]:=
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ap = ArcPresentation[K]
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Out[13]=
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ArcPresentation[{12, 2}, {1, 10}, {6, 11}, {10, 12}, {3, 7}, {2, 5}, {9, 6}, {7, 4}, {11, 8}, {5, 9}, {8, 3}, {4, 1}] |
In[14]:=
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Draw[ap]
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Out[14]=
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-Graphics- |
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-22 t+31-22 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4+z^2+1 }[/math] |
| 2nd Alexander ideal (db, data sources) | [math]\displaystyle{ \{1\} }[/math] |
| Determinant and Signature | { 93, 0 } |
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-14 q+16-15 q^{-1} +12 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| HOMFLY-PT polynomial (db, data sources) | [math]\displaystyle{ -z^6+2 a^2 z^4+2 z^4 a^{-2} -2 z^4-a^4 z^2+2 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} -2 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial (db, data sources) | [math]\displaystyle{ 2 a z^9+2 z^9 a^{-1} +6 a^2 z^8+5 z^8 a^{-2} +11 z^8+7 a^3 z^7+11 a z^7+9 z^7 a^{-1} +5 z^7 a^{-3} +4 a^4 z^6-5 a^2 z^6-4 z^6 a^{-2} +3 z^6 a^{-4} -16 z^6+a^5 z^5-12 a^3 z^5-27 a z^5-22 z^5 a^{-1} -7 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4-4 a^2 z^4-2 z^4 a^{-2} -5 z^4 a^{-4} +5 z^4-a^5 z^3+6 a^3 z^3+17 a z^3+15 z^3 a^{-1} +3 z^3 a^{-3} -2 z^3 a^{-5} +2 a^4 z^2+2 a^2 z^2+3 z^2 a^{-2} +3 z^2 a^{-4} -a^3 z-3 a z-3 z a^{-1} +z a^{-5} -2 a^{-2} - a^{-4} }[/math] |
| The A2 invariant | [math]\displaystyle{ -q^{16}+q^{14}+2 q^{12}-3 q^{10}+2 q^8-q^6-2 q^4+3 q^2-2+4 q^{-2} - q^{-4} + q^{-6} +3 q^{-8} -3 q^{-10} + q^{-12} - q^{-16} }[/math] |
| The G2 invariant | [math]\displaystyle{ q^{80}-3 q^{78}+7 q^{76}-13 q^{74}+15 q^{72}-14 q^{70}+3 q^{68}+22 q^{66}-52 q^{64}+86 q^{62}-103 q^{60}+81 q^{58}-21 q^{56}-81 q^{54}+193 q^{52}-265 q^{50}+263 q^{48}-160 q^{46}-20 q^{44}+222 q^{42}-364 q^{40}+386 q^{38}-262 q^{36}+37 q^{34}+184 q^{32}-320 q^{30}+303 q^{28}-144 q^{26}-75 q^{24}+258 q^{22}-309 q^{20}+196 q^{18}+30 q^{16}-286 q^{14}+447 q^{12}-447 q^{10}+279 q^8-290 q^4+500 q^2-540+409 q^{-2} -151 q^{-4} -144 q^{-6} +361 q^{-8} -422 q^{-10} +318 q^{-12} -95 q^{-14} -130 q^{-16} +276 q^{-18} -268 q^{-20} +115 q^{-22} +106 q^{-24} -293 q^{-26} +355 q^{-28} -262 q^{-30} +54 q^{-32} +177 q^{-34} -333 q^{-36} +372 q^{-38} -279 q^{-40} +115 q^{-42} +54 q^{-44} -183 q^{-46} +223 q^{-48} -191 q^{-50} +117 q^{-52} -32 q^{-54} -29 q^{-56} +60 q^{-58} -67 q^{-60} +53 q^{-62} -33 q^{-64} +13 q^{-66} + q^{-68} -9 q^{-70} +9 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80} }[/math] |
Further Quantum Invariants
Further quantum knot invariants for 10_107.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | [math]\displaystyle{ -q^{11}+3 q^9-4 q^7+4 q^5-3 q^3+q+2 q^{-1} -2 q^{-3} +5 q^{-5} -4 q^{-7} +2 q^{-9} - q^{-11} }[/math] |
| 2 | [math]\displaystyle{ q^{32}-3 q^{30}+11 q^{26}-13 q^{24}-11 q^{22}+34 q^{20}-13 q^{18}-36 q^{16}+44 q^{14}+6 q^{12}-46 q^{10}+26 q^8+22 q^6-29 q^4-6 q^2+24+4 q^{-2} -34 q^{-4} +15 q^{-6} +36 q^{-8} -43 q^{-10} -5 q^{-12} +47 q^{-14} -27 q^{-16} -19 q^{-18} +28 q^{-20} -5 q^{-22} -11 q^{-24} +7 q^{-26} -2 q^{-30} + q^{-32} }[/math] |
| 3 | [math]\displaystyle{ -q^{63}+3 q^{61}-7 q^{57}-2 q^{55}+17 q^{53}+14 q^{51}-40 q^{49}-38 q^{47}+59 q^{45}+92 q^{43}-62 q^{41}-174 q^{39}+34 q^{37}+257 q^{35}+44 q^{33}-315 q^{31}-159 q^{29}+327 q^{27}+272 q^{25}-281 q^{23}-358 q^{21}+188 q^{19}+399 q^{17}-82 q^{15}-384 q^{13}-18 q^{11}+328 q^9+115 q^7-253 q^5-188 q^3+159 q+257 q^{-1} -64 q^{-3} -308 q^{-5} -47 q^{-7} +342 q^{-9} +162 q^{-11} -341 q^{-13} -267 q^{-15} +293 q^{-17} +351 q^{-19} -201 q^{-21} -384 q^{-23} +85 q^{-25} +365 q^{-27} +11 q^{-29} -282 q^{-31} -86 q^{-33} +188 q^{-35} +104 q^{-37} -100 q^{-39} -83 q^{-41} +37 q^{-43} +52 q^{-45} -10 q^{-47} -26 q^{-49} +3 q^{-51} +10 q^{-53} - q^{-55} -3 q^{-57} +2 q^{-61} - q^{-63} }[/math] |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ -q^{16}+q^{14}+2 q^{12}-3 q^{10}+2 q^8-q^6-2 q^4+3 q^2-2+4 q^{-2} - q^{-4} + q^{-6} +3 q^{-8} -3 q^{-10} + q^{-12} - q^{-16} }[/math] |
| 2,0 | [math]\displaystyle{ q^{42}-q^{40}-3 q^{38}+q^{36}+7 q^{34}+2 q^{32}-13 q^{30}-5 q^{28}+17 q^{26}+5 q^{24}-20 q^{22}-6 q^{20}+22 q^{18}+8 q^{16}-24 q^{14}+q^{12}+21 q^{10}-6 q^8-11 q^6+5 q^4+3 q^2-10+6 q^{-2} +8 q^{-4} -13 q^{-6} -3 q^{-8} +24 q^{-10} +5 q^{-12} -26 q^{-14} +6 q^{-16} +22 q^{-18} -4 q^{-20} -20 q^{-22} +15 q^{-26} -3 q^{-28} -9 q^{-30} + q^{-32} +4 q^{-34} -2 q^{-38} + q^{-42} }[/math] |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | [math]\displaystyle{ q^{34}-3 q^{32}+q^{30}+7 q^{28}-13 q^{26}+4 q^{24}+19 q^{22}-28 q^{20}+6 q^{18}+28 q^{16}-36 q^{14}+4 q^{12}+28 q^{10}-24 q^8-4 q^6+16 q^4-q^2-9-4 q^{-2} +21 q^{-4} -4 q^{-6} -23 q^{-8} +34 q^{-10} +2 q^{-12} -33 q^{-14} +30 q^{-16} -25 q^{-20} +16 q^{-22} + q^{-24} -10 q^{-26} +5 q^{-28} + q^{-30} -2 q^{-32} + q^{-34} }[/math] |
| 1,0,0 | [math]\displaystyle{ -q^{21}+q^{19}+2 q^{15}-3 q^{13}+3 q^{11}-3 q^9+q^7-2 q^5+2 q^3+3 q^{-3} - q^{-5} +3 q^{-7} - q^{-9} +4 q^{-11} -3 q^{-13} + q^{-15} - q^{-17} - q^{-21} }[/math] |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ -q^{34}+3 q^{32}-7 q^{30}+13 q^{28}-21 q^{26}+30 q^{24}-37 q^{22}+42 q^{20}-42 q^{18}+36 q^{16}-24 q^{14}+8 q^{12}+12 q^{10}-34 q^8+54 q^6-70 q^4+79 q^2-81+74 q^{-2} -59 q^{-4} +42 q^{-6} -19 q^{-8} +20 q^{-12} -31 q^{-14} +40 q^{-16} -42 q^{-18} +39 q^{-20} -32 q^{-22} +23 q^{-24} -16 q^{-26} +9 q^{-28} -5 q^{-30} +2 q^{-32} - q^{-34} }[/math] |
| 1,0 | [math]\displaystyle{ q^{56}-3 q^{52}-3 q^{50}+4 q^{48}+10 q^{46}-17 q^{42}-12 q^{40}+18 q^{38}+28 q^{36}-6 q^{34}-39 q^{32}-15 q^{30}+37 q^{28}+34 q^{26}-22 q^{24}-44 q^{22}+q^{20}+42 q^{18}+15 q^{16}-32 q^{14}-22 q^{12}+22 q^{10}+25 q^8-14 q^6-27 q^4+7 q^2+29- q^{-2} -30 q^{-4} -5 q^{-6} +31 q^{-8} +17 q^{-10} -29 q^{-12} -27 q^{-14} +24 q^{-16} +43 q^{-18} -7 q^{-20} -45 q^{-22} -14 q^{-24} +37 q^{-26} +30 q^{-28} -19 q^{-30} -35 q^{-32} -2 q^{-34} +24 q^{-36} +12 q^{-38} -10 q^{-40} -13 q^{-42} +7 q^{-46} +3 q^{-48} -2 q^{-50} -2 q^{-52} + q^{-56} }[/math] |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ q^{80}-3 q^{78}+7 q^{76}-13 q^{74}+15 q^{72}-14 q^{70}+3 q^{68}+22 q^{66}-52 q^{64}+86 q^{62}-103 q^{60}+81 q^{58}-21 q^{56}-81 q^{54}+193 q^{52}-265 q^{50}+263 q^{48}-160 q^{46}-20 q^{44}+222 q^{42}-364 q^{40}+386 q^{38}-262 q^{36}+37 q^{34}+184 q^{32}-320 q^{30}+303 q^{28}-144 q^{26}-75 q^{24}+258 q^{22}-309 q^{20}+196 q^{18}+30 q^{16}-286 q^{14}+447 q^{12}-447 q^{10}+279 q^8-290 q^4+500 q^2-540+409 q^{-2} -151 q^{-4} -144 q^{-6} +361 q^{-8} -422 q^{-10} +318 q^{-12} -95 q^{-14} -130 q^{-16} +276 q^{-18} -268 q^{-20} +115 q^{-22} +106 q^{-24} -293 q^{-26} +355 q^{-28} -262 q^{-30} +54 q^{-32} +177 q^{-34} -333 q^{-36} +372 q^{-38} -279 q^{-40} +115 q^{-42} +54 q^{-44} -183 q^{-46} +223 q^{-48} -191 q^{-50} +117 q^{-52} -32 q^{-54} -29 q^{-56} +60 q^{-58} -67 q^{-60} +53 q^{-62} -33 q^{-64} +13 q^{-66} + q^{-68} -9 q^{-70} +9 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80} }[/math] |
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Computer Talk
The above data is available with the Mathematica package
KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["10 107"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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[math]\displaystyle{ -t^3+8 t^2-22 t+31-22 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
In[5]:=
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Conway[K][z]
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Out[5]=
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[math]\displaystyle{ -z^6+2 z^4+z^2+1 }[/math] |
In[6]:=
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Alexander[K, 2][t]
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KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
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Out[6]=
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[math]\displaystyle{ \{1\} }[/math] |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 93, 0 } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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[math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-14 q+16-15 q^{-1} +12 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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[math]\displaystyle{ -z^6+2 a^2 z^4+2 z^4 a^{-2} -2 z^4-a^4 z^2+2 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} -2 z^2+2 a^{-2} - a^{-4} }[/math] |
In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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[math]\displaystyle{ 2 a z^9+2 z^9 a^{-1} +6 a^2 z^8+5 z^8 a^{-2} +11 z^8+7 a^3 z^7+11 a z^7+9 z^7 a^{-1} +5 z^7 a^{-3} +4 a^4 z^6-5 a^2 z^6-4 z^6 a^{-2} +3 z^6 a^{-4} -16 z^6+a^5 z^5-12 a^3 z^5-27 a z^5-22 z^5 a^{-1} -7 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4-4 a^2 z^4-2 z^4 a^{-2} -5 z^4 a^{-4} +5 z^4-a^5 z^3+6 a^3 z^3+17 a z^3+15 z^3 a^{-1} +3 z^3 a^{-3} -2 z^3 a^{-5} +2 a^4 z^2+2 a^2 z^2+3 z^2 a^{-2} +3 z^2 a^{-4} -a^3 z-3 a z-3 z a^{-1} +z a^{-5} -2 a^{-2} - a^{-4} }[/math] |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, [math]\displaystyle{ q\leftrightarrow q^{-1} }[/math]): {}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 107"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ [math]\displaystyle{ -t^3+8 t^2-22 t+31-22 t^{-1} +8 t^{-2} - t^{-3} }[/math], [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-14 q+16-15 q^{-1} +12 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{} |
Vassiliev invariants
| V2 and V3: | (1, 1) |
| V2,1 through V6,9: |
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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 [math]\displaystyle{ t^rq^j }[/math] are shown, along with their alternating sums [math]\displaystyle{ \chi }[/math] (fixed [math]\displaystyle{ j }[/math], alternation over [math]\displaystyle{ r }[/math]). The squares with yellow highlighting are those on the "critical diagonals", where [math]\displaystyle{ j-2r=s+1 }[/math] or [math]\displaystyle{ j-2r=s-1 }[/math], where [math]\displaystyle{ s= }[/math]0 is the signature of 10 107. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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| Integral Khovanov Homology
(db, data source) |
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The Coloured Jones Polynomials
The Coloured Jones Polynomials (in the [math]\displaystyle{ n+1 }[/math]-dimensional representation of [math]\displaystyle{ sl(2) }[/math])
| [math]\displaystyle{ n }[/math] | [math]\displaystyle{ J_n }[/math] |
| 2 | [math]\displaystyle{ q^{15}-3 q^{14}+2 q^{13}+8 q^{12}-21 q^{11}+8 q^{10}+41 q^9-68 q^8+115 q^6-120 q^5-38 q^4+194 q^3-141 q^2-87 q+232-121 q^{-1} -117 q^{-2} +209 q^{-3} -70 q^{-4} -113 q^{-5} +137 q^{-6} -18 q^{-7} -75 q^{-8} +57 q^{-9} +5 q^{-10} -28 q^{-11} +12 q^{-12} +3 q^{-13} -4 q^{-14} + q^{-15} }[/math] |
| 3 | [math]\displaystyle{ -q^{30}+3 q^{29}-2 q^{28}-3 q^{27}+q^{26}+14 q^{25}-9 q^{24}-32 q^{23}+17 q^{22}+76 q^{21}-24 q^{20}-152 q^{19}+280 q^{17}+60 q^{16}-426 q^{15}-196 q^{14}+573 q^{13}+414 q^{12}-706 q^{11}-665 q^{10}+756 q^9+966 q^8-764 q^7-1225 q^6+682 q^5+1469 q^4-584 q^3-1614 q^2+421 q+1713-263 q^{-1} -1712 q^{-2} +74 q^{-3} +1648 q^{-4} +105 q^{-5} -1499 q^{-6} -272 q^{-7} +1282 q^{-8} +407 q^{-9} -1018 q^{-10} -483 q^{-11} +736 q^{-12} +484 q^{-13} -465 q^{-14} -428 q^{-15} +250 q^{-16} +328 q^{-17} -106 q^{-18} -215 q^{-19} +27 q^{-20} +120 q^{-21} +6 q^{-22} -61 q^{-23} -6 q^{-24} +23 q^{-25} +4 q^{-26} -7 q^{-27} -3 q^{-28} +4 q^{-29} - q^{-30} }[/math] |
| 4 | [math]\displaystyle{ q^{50}-3 q^{49}+2 q^{48}+3 q^{47}-6 q^{46}+6 q^{45}-13 q^{44}+15 q^{43}+21 q^{42}-42 q^{41}-q^{40}-45 q^{39}+96 q^{38}+138 q^{37}-149 q^{36}-151 q^{35}-260 q^{34}+330 q^{33}+694 q^{32}-90 q^{31}-609 q^{30}-1281 q^{29}+319 q^{28}+2052 q^{27}+1043 q^{26}-782 q^{25}-3636 q^{24}-1189 q^{23}+3436 q^{22}+3898 q^{21}+884 q^{20}-6369 q^{19}-4885 q^{18}+3065 q^{17}+7369 q^{16}+4989 q^{15}-7525 q^{14}-9427 q^{13}+286 q^{12}+9469 q^{11}+10039 q^{10}-6397 q^9-12745 q^8-3593 q^7+9462 q^6+14012 q^5-3925 q^4-13971 q^3-7011 q^2+7925 q+16069-1101 q^{-1} -13328 q^{-2} -9408 q^{-3} +5386 q^{-4} +16197 q^{-5} +1818 q^{-6} -10982 q^{-7} -10666 q^{-8} +1973 q^{-9} +14263 q^{-10} +4470 q^{-11} -7006 q^{-12} -10208 q^{-13} -1651 q^{-14} +10202 q^{-15} +5740 q^{-16} -2377 q^{-17} -7599 q^{-18} -3896 q^{-19} +5182 q^{-20} +4758 q^{-21} +904 q^{-22} -3850 q^{-23} -3702 q^{-24} +1377 q^{-25} +2416 q^{-26} +1706 q^{-27} -1013 q^{-28} -2035 q^{-29} -111 q^{-30} +597 q^{-31} +996 q^{-32} +39 q^{-33} -661 q^{-34} -181 q^{-35} -17 q^{-36} +305 q^{-37} +101 q^{-38} -133 q^{-39} -34 q^{-40} -45 q^{-41} +54 q^{-42} +26 q^{-43} -22 q^{-44} + q^{-45} -9 q^{-46} +7 q^{-47} +3 q^{-48} -4 q^{-49} + q^{-50} }[/math] |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Rolfsen Knot Page master template (intermediate). See/edit the Rolfsen_Splice_Base (expert). Back to the top. |
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