10 120
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 120's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
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Knot presentations
| Planar diagram presentation | X1627 X5,18,6,19 X13,20,14,1 X11,16,12,17 X3,10,4,11 X7,12,8,13 X9,4,10,5 X15,8,16,9 X19,14,20,15 X17,2,18,3 |
| Gauss code | -1, 10, -5, 7, -2, 1, -6, 8, -7, 5, -4, 6, -3, 9, -8, 4, -10, 2, -9, 3 |
| Dowker-Thistlethwaite code | 6 10 18 12 4 16 20 8 2 14 |
| Conway Notation | [8*20::20] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 14, width is 5, Braid index is 5 |
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 [{13, 6}, {2, 11}, {7, 12}, {5, 1}, {6, 4}, {10, 5}, {11, 9}, {8, 10}, {9, 13}, {3, 7}, {4, 8}, {12, 2}, {1, 3}] |
[edit Notes on presentations of 10 120]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 120"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1627 X5,18,6,19 X13,20,14,1 X11,16,12,17 X3,10,4,11 X7,12,8,13 X9,4,10,5 X15,8,16,9 X19,14,20,15 X17,2,18,3 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 10, -5, 7, -2, 1, -6, 8, -7, 5, -4, 6, -3, 9, -8, 4, -10, 2, -9, 3 |
In[6]:=
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DTCode[K]
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Out[6]=
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6 10 18 12 4 16 20 8 2 14 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$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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[8*20::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,-1,-4,-3,-2,-2,-3,-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, 14, 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[{13, 6}, {2, 11}, {7, 12}, {5, 1}, {6, 4}, {10, 5}, {11, 9}, {8, 10}, {9, 13}, {3, 7}, {4, 8}, {12, 2}, {1, 3}] |
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{ 8 t^2-26 t+37-26 t^{-1} +8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^4+6 z^2+1 }[/math] |
| 2nd Alexander ideal (db, data sources) | [math]\displaystyle{ \{1\} }[/math] |
| Determinant and Signature | { 105, -4 } |
| Jones polynomial | [math]\displaystyle{ q^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +17 q^{-6} -18 q^{-7} +16 q^{-8} -13 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12} }[/math] |
| HOMFLY-PT polynomial (db, data sources) | [math]\displaystyle{ a^{12}-4 z^2 a^{10}-3 a^{10}+3 z^4 a^8+3 z^2 a^8+4 z^4 a^6+7 z^2 a^6+3 a^6+z^4 a^4 }[/math] |
| Kauffman polynomial (db, data sources) | [math]\displaystyle{ z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-10 z^5 a^{13}+8 z^3 a^{13}-2 z a^{13}+6 z^8 a^{12}-13 z^6 a^{12}+6 z^4 a^{12}+z^2 a^{12}+a^{12}+3 z^9 a^{11}+7 z^7 a^{11}-33 z^5 a^{11}+29 z^3 a^{11}-8 z a^{11}+16 z^8 a^{10}-33 z^6 a^{10}+17 z^4 a^{10}-7 z^2 a^{10}+3 a^{10}+3 z^9 a^9+16 z^7 a^9-44 z^5 a^9+26 z^3 a^9-4 z a^9+10 z^8 a^8-9 z^6 a^8-3 z^4 a^8+13 z^7 a^7-17 z^5 a^7+5 z^3 a^7+2 z a^7+10 z^6 a^6-11 z^4 a^6+7 z^2 a^6-3 a^6+4 z^5 a^5+z^4 a^4 }[/math] |
| The A2 invariant | [math]\displaystyle{ q^{38}+q^{36}-3 q^{34}+q^{32}-5 q^{28}+2 q^{26}-2 q^{24}+q^{22}+2 q^{20}-q^{18}+5 q^{16}-2 q^{14}+2 q^{12}+3 q^{10}-3 q^8+q^6 }[/math] |
| The G2 invariant | [math]\displaystyle{ q^{190}-3 q^{188}+8 q^{186}-16 q^{184}+21 q^{182}-23 q^{180}+9 q^{178}+25 q^{176}-74 q^{174}+131 q^{172}-159 q^{170}+124 q^{168}-16 q^{166}-151 q^{164}+326 q^{162}-410 q^{160}+358 q^{158}-152 q^{156}-149 q^{154}+426 q^{152}-569 q^{150}+496 q^{148}-227 q^{146}-123 q^{144}+405 q^{142}-489 q^{140}+345 q^{138}-47 q^{136}-260 q^{134}+434 q^{132}-410 q^{130}+162 q^{128}+180 q^{126}-491 q^{124}+639 q^{122}-549 q^{120}+251 q^{118}+157 q^{116}-531 q^{114}+731 q^{112}-704 q^{110}+430 q^{108}-19 q^{106}-371 q^{104}+597 q^{102}-569 q^{100}+321 q^{98}+41 q^{96}-335 q^{94}+427 q^{92}-308 q^{90}+21 q^{88}+288 q^{86}-464 q^{84}+445 q^{82}-224 q^{80}-79 q^{78}+349 q^{76}-482 q^{74}+440 q^{72}-267 q^{70}+46 q^{68}+153 q^{66}-266 q^{64}+286 q^{62}-215 q^{60}+119 q^{58}-14 q^{56}-56 q^{54}+84 q^{52}-91 q^{50}+68 q^{48}-38 q^{46}+13 q^{44}+7 q^{42}-12 q^{40}+12 q^{38}-10 q^{36}+6 q^{34}-3 q^{32}+q^{30} }[/math] |
Further Quantum Invariants
Further quantum knot invariants for 10_120.
A1 Invariants.
| Weight | Invariant |
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| 1 | [math]\displaystyle{ q^{25}-3 q^{23}+4 q^{21}-5 q^{19}+3 q^{17}-2 q^{15}-q^{13}+4 q^{11}-3 q^9+6 q^7-3 q^5+q^3 }[/math] |
| 2 | [math]\displaystyle{ q^{70}-3 q^{68}-q^{66}+13 q^{64}-10 q^{62}-20 q^{60}+35 q^{58}+3 q^{56}-52 q^{54}+36 q^{52}+33 q^{50}-58 q^{48}+10 q^{46}+45 q^{44}-33 q^{42}-20 q^{40}+31 q^{38}+8 q^{36}-39 q^{34}-q^{32}+49 q^{30}-34 q^{28}-33 q^{26}+62 q^{24}-9 q^{22}-41 q^{20}+36 q^{18}+5 q^{16}-20 q^{14}+9 q^{12}+3 q^{10}-3 q^8+q^6 }[/math] |
| 3 | [math]\displaystyle{ q^{135}-3 q^{133}-q^{131}+8 q^{129}+8 q^{127}-18 q^{125}-34 q^{123}+28 q^{121}+81 q^{119}-5 q^{117}-149 q^{115}-69 q^{113}+203 q^{111}+194 q^{109}-198 q^{107}-344 q^{105}+112 q^{103}+474 q^{101}+35 q^{99}-525 q^{97}-217 q^{95}+496 q^{93}+374 q^{91}-400 q^{89}-477 q^{87}+262 q^{85}+518 q^{83}-120 q^{81}-507 q^{79}-9 q^{77}+462 q^{75}+135 q^{73}-379 q^{71}-260 q^{69}+287 q^{67}+369 q^{65}-143 q^{63}-477 q^{61}-25 q^{59}+518 q^{57}+214 q^{55}-507 q^{53}-381 q^{51}+404 q^{49}+479 q^{47}-253 q^{45}-490 q^{43}+100 q^{41}+415 q^{39}+18 q^{37}-294 q^{35}-57 q^{33}+165 q^{31}+68 q^{29}-87 q^{27}-39 q^{25}+40 q^{23}+18 q^{21}-13 q^{19}-8 q^{17}+6 q^{15}+3 q^{13}-3 q^{11}+q^9 }[/math] |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ q^{38}+q^{36}-3 q^{34}+q^{32}-5 q^{28}+2 q^{26}-2 q^{24}+q^{22}+2 q^{20}-q^{18}+5 q^{16}-2 q^{14}+2 q^{12}+3 q^{10}-3 q^8+q^6 }[/math] |
| 2,0 | [math]\displaystyle{ q^{96}+q^{94}-2 q^{92}-4 q^{90}+10 q^{86}-q^{84}-15 q^{82}-5 q^{80}+20 q^{78}+14 q^{76}-27 q^{74}-12 q^{72}+28 q^{70}+22 q^{68}-21 q^{66}-16 q^{64}+25 q^{62}+8 q^{60}-22 q^{58}-13 q^{56}+8 q^{54}-9 q^{52}-7 q^{50}+4 q^{48}-10 q^{46}-9 q^{44}+19 q^{42}+20 q^{40}-26 q^{38}-9 q^{36}+38 q^{34}+13 q^{32}-33 q^{30}-8 q^{28}+29 q^{26}+10 q^{24}-19 q^{22}-5 q^{20}+11 q^{18}-3 q^{14}+q^{12} }[/math] |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | [math]\displaystyle{ q^{80}-3 q^{78}+2 q^{76}+5 q^{74}-15 q^{72}+11 q^{70}+11 q^{68}-32 q^{66}+26 q^{64}+17 q^{62}-40 q^{60}+29 q^{58}+15 q^{56}-39 q^{54}+9 q^{52}+14 q^{50}-18 q^{48}-9 q^{46}+3 q^{44}+14 q^{42}-21 q^{40}-14 q^{38}+43 q^{36}-22 q^{34}-17 q^{32}+49 q^{30}-15 q^{28}-18 q^{26}+31 q^{24}-8 q^{22}-12 q^{20}+11 q^{18}-3 q^{14}+q^{12} }[/math] |
| 1,0,0 | [math]\displaystyle{ q^{51}+q^{49}+q^{47}-3 q^{45}+q^{43}-3 q^{41}-5 q^{37}+2 q^{35}-3 q^{33}+q^{31}+q^{29}+2 q^{27}+2 q^{25}+5 q^{21}-2 q^{19}+3 q^{17}-q^{15}+3 q^{13}-3 q^{11}+q^9 }[/math] |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ q^{80}-3 q^{78}+8 q^{76}-15 q^{74}+25 q^{72}-37 q^{70}+45 q^{68}-52 q^{66}+54 q^{64}-47 q^{62}+34 q^{60}-15 q^{58}-11 q^{56}+37 q^{54}-65 q^{52}+84 q^{50}-100 q^{48}+103 q^{46}-97 q^{44}+80 q^{42}-57 q^{40}+32 q^{38}-3 q^{36}-18 q^{34}+39 q^{32}-49 q^{30}+55 q^{28}-50 q^{26}+43 q^{24}-32 q^{22}+24 q^{20}-13 q^{18}+6 q^{16}-3 q^{14}+q^{12} }[/math] |
| 1,0 | [math]\displaystyle{ q^{130}-3 q^{126}-3 q^{124}+5 q^{122}+10 q^{120}-3 q^{118}-20 q^{116}-9 q^{114}+27 q^{112}+27 q^{110}-20 q^{108}-45 q^{106}-q^{104}+55 q^{102}+29 q^{100}-43 q^{98}-47 q^{96}+21 q^{94}+56 q^{92}+3 q^{90}-49 q^{88}-21 q^{86}+34 q^{84}+25 q^{82}-25 q^{80}-31 q^{78}+16 q^{76}+32 q^{74}-12 q^{72}-41 q^{70}+q^{68}+41 q^{66}+8 q^{64}-44 q^{62}-26 q^{60}+40 q^{58}+42 q^{56}-23 q^{54}-53 q^{52}+5 q^{50}+56 q^{48}+26 q^{46}-35 q^{44}-37 q^{42}+13 q^{40}+37 q^{38}+9 q^{36}-20 q^{34}-18 q^{32}+5 q^{30}+12 q^{28}+3 q^{26}-3 q^{24}-3 q^{22}+q^{18} }[/math] |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ q^{190}-3 q^{188}+8 q^{186}-16 q^{184}+21 q^{182}-23 q^{180}+9 q^{178}+25 q^{176}-74 q^{174}+131 q^{172}-159 q^{170}+124 q^{168}-16 q^{166}-151 q^{164}+326 q^{162}-410 q^{160}+358 q^{158}-152 q^{156}-149 q^{154}+426 q^{152}-569 q^{150}+496 q^{148}-227 q^{146}-123 q^{144}+405 q^{142}-489 q^{140}+345 q^{138}-47 q^{136}-260 q^{134}+434 q^{132}-410 q^{130}+162 q^{128}+180 q^{126}-491 q^{124}+639 q^{122}-549 q^{120}+251 q^{118}+157 q^{116}-531 q^{114}+731 q^{112}-704 q^{110}+430 q^{108}-19 q^{106}-371 q^{104}+597 q^{102}-569 q^{100}+321 q^{98}+41 q^{96}-335 q^{94}+427 q^{92}-308 q^{90}+21 q^{88}+288 q^{86}-464 q^{84}+445 q^{82}-224 q^{80}-79 q^{78}+349 q^{76}-482 q^{74}+440 q^{72}-267 q^{70}+46 q^{68}+153 q^{66}-266 q^{64}+286 q^{62}-215 q^{60}+119 q^{58}-14 q^{56}-56 q^{54}+84 q^{52}-91 q^{50}+68 q^{48}-38 q^{46}+13 q^{44}+7 q^{42}-12 q^{40}+12 q^{38}-10 q^{36}+6 q^{34}-3 q^{32}+q^{30} }[/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["10 120"];
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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{ 8 t^2-26 t+37-26 t^{-1} +8 t^{-2} }[/math] |
In[5]:=
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Conway[K][z]
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Out[5]=
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[math]\displaystyle{ 8 z^4+6 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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{ 105, -4 } |
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^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +17 q^{-6} -18 q^{-7} +16 q^{-8} -13 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12} }[/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{ a^{12}-4 z^2 a^{10}-3 a^{10}+3 z^4 a^8+3 z^2 a^8+4 z^4 a^6+7 z^2 a^6+3 a^6+z^4 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{ z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-10 z^5 a^{13}+8 z^3 a^{13}-2 z a^{13}+6 z^8 a^{12}-13 z^6 a^{12}+6 z^4 a^{12}+z^2 a^{12}+a^{12}+3 z^9 a^{11}+7 z^7 a^{11}-33 z^5 a^{11}+29 z^3 a^{11}-8 z a^{11}+16 z^8 a^{10}-33 z^6 a^{10}+17 z^4 a^{10}-7 z^2 a^{10}+3 a^{10}+3 z^9 a^9+16 z^7 a^9-44 z^5 a^9+26 z^3 a^9-4 z a^9+10 z^8 a^8-9 z^6 a^8-3 z^4 a^8+13 z^7 a^7-17 z^5 a^7+5 z^3 a^7+2 z a^7+10 z^6 a^6-11 z^4 a^6+7 z^2 a^6-3 a^6+4 z^5 a^5+z^4 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["10 120"];
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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{ 8 t^2-26 t+37-26 t^{-1} +8 t^{-2} }[/math], [math]\displaystyle{ q^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +17 q^{-6} -18 q^{-7} +16 q^{-8} -13 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12} }[/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: | (6, -13) |
| 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]-4 is the signature of 10 120. 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^{-4} -4 q^{-5} +6 q^{-6} +7 q^{-7} -33 q^{-8} +31 q^{-9} +38 q^{-10} -110 q^{-11} +63 q^{-12} +109 q^{-13} -205 q^{-14} +62 q^{-15} +192 q^{-16} -255 q^{-17} +24 q^{-18} +239 q^{-19} -232 q^{-20} -27 q^{-21} +226 q^{-22} -154 q^{-23} -62 q^{-24} +158 q^{-25} -63 q^{-26} -59 q^{-27} +70 q^{-28} -8 q^{-29} -27 q^{-30} +15 q^{-31} +2 q^{-32} -4 q^{-33} + q^{-34} }[/math] |
| 3 | [math]\displaystyle{ q^{-6} -4 q^{-7} +6 q^{-8} +3 q^{-9} -13 q^{-10} -9 q^{-11} +37 q^{-12} +25 q^{-13} -92 q^{-14} -57 q^{-15} +192 q^{-16} +122 q^{-17} -314 q^{-18} -294 q^{-19} +504 q^{-20} +519 q^{-21} -629 q^{-22} -884 q^{-23} +741 q^{-24} +1251 q^{-25} -704 q^{-26} -1669 q^{-27} +615 q^{-28} +1972 q^{-29} -400 q^{-30} -2212 q^{-31} +163 q^{-32} +2306 q^{-33} +112 q^{-34} -2294 q^{-35} -384 q^{-36} +2187 q^{-37} +626 q^{-38} -1967 q^{-39} -855 q^{-40} +1689 q^{-41} +1013 q^{-42} -1329 q^{-43} -1111 q^{-44} +950 q^{-45} +1090 q^{-46} -555 q^{-47} -989 q^{-48} +237 q^{-49} +782 q^{-50} +5 q^{-51} -550 q^{-52} -125 q^{-53} +326 q^{-54} +151 q^{-55} -158 q^{-56} -116 q^{-57} +54 q^{-58} +71 q^{-59} -14 q^{-60} -30 q^{-61} + q^{-62} +9 q^{-63} +2 q^{-64} -4 q^{-65} + q^{-66} }[/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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