10 89
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 89's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_89's page at Knotilus! Visit 10 89's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X4251 X12,8,13,7 X8394 X2,9,3,10 X20,13,1,14 X14,5,15,6 X6,19,7,20 X18,16,19,15 X16,11,17,12 X10,17,11,18 |
| Gauss code | 1, -4, 3, -1, 6, -7, 2, -3, 4, -10, 9, -2, 5, -6, 8, -9, 10, -8, 7, -5 |
| Dowker-Thistlethwaite code | 4 8 14 12 2 16 20 18 10 6 |
| Conway Notation | [.21.210] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 | 
|  [{3, 10}, {6, 2}, {1, 3}, {5, 8}, {7, 9}, {8, 11}, {10, 6}, {12, 7}, {11, 4}, {2, 5}, {4, 12}, {9, 1}] |
[edit Notes on presentations of 10 89]
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]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["10 89"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X4251 X12,8,13,7 X8394 X2,9,3,10 X20,13,1,14 X14,5,15,6 X6,19,7,20 X18,16,19,15 X16,11,17,12 X10,17,11,18 |
In[5]:=
| GaussCode[K]
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Out[5]=
| 1, -4, 3, -1, 6, -7, 2, -3, 4, -10, 9, -2, 5, -6, 8, -9, 10, -8, 7, -5 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 8 14 12 2 16 20 18 10 6 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [.21.210] |
In[9]:=
| 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]=
| BR(5,{−1,2,−1,2,3,−2,−1,−4,−3,2,−3,−4}) |
In[10]:=
| {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]=
| { 5, 12, 5 } |
In[11]:=
| Show[BraidPlot[br]]
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Out[11]=
| -Graphics- |
In[12]:=
| 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]=
| -Graphics- |
In[13]:=
| ap = ArcPresentation[K]
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Out[13]=
| ArcPresentation[{3, 10}, {6, 2}, {1, 3}, {5, 8}, {7, 9}, {8, 11}, {10, 6}, {12, 7}, {11, 4}, {2, 5}, {4, 12}, {9, 1}] |
In[14]:=
| Draw[ap]
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|
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Out[14]=
| -Graphics- |
[edit] Three dimensional invariants
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[edit] Four dimensional invariants
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[edit] Polynomial invariants
| Alexander polynomial | t3−8t2 + 24t−33 + 24t−1−8t−2 + t−3 |
| Conway polynomial | z6−2z4 + z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 99, -2 } |
| Jones polynomial | −q2 + 5q−9 + 13q−1−16q−2 + 17q−3−15q−4 + 12q−5−7q−6 + 3q−7−q−8 |
| HOMFLY-PT polynomial (db, data sources) | −a8 + 3z2a6 + 2a6−3z4a4−4z2a4−a4 + z6a2 + 2z4a2 + 2z2a2−z4 + 1 |
| Kauffman polynomial (db, data sources) | z5a9−2z3a9 + za9 + 3z6a8−5z4a8 + 3z2a8−a8 + 5z7a7−7z5a7 + 4z3a7−za7 + 5z8a6−3z6a6−4z4a6 + 6z2a6−2a6 + 2z9a5 + 11z7a5−27z5a5 + 20z3a5−4za5 + 12z8a4−15z6a4−2z4a4 + 6z2a4−a4 + 2z9a3 + 15z7a3−35z5a3 + 19z3a3−2za3 + 7z8a2−4z6a2−9z4a2 + 3z2a2 + 9z7a−15z5a + 5z3a + 5z6−6z4 + 1 + z5a−1 |
| The A2 invariant | −q26−q24 + 2q22−q20−q18 + 4q16−2q14 + 2q12−2q8 + 2q6−4q4 + 4q2−q−2 + 3q−4−q−6 |
| The G2 invariant | q128−2q126 + 5q124−8q122 + 9q120−9q118 + q116 + 13q114−32q112 + 52q110−67q108 + 62q106−34q104−26q102 + 111q100−190q98 + 234q96−208q94 + 89q92 + 87q90−276q88 + 405q86−402q84 + 261q82−14q80−243q78 + 405q76−399q74 + 229q72 + 28q70−252q68 + 332q66−238q64 + 7q62 + 270q60−447q58 + 447q56−250q54−76q52 + 406q50−617q48 + 623q46−423q44 + 92q42 + 264q40−515q38 + 577q36−433q34 + 148q32 + 148q30−350q28 + 361q26−198q24−53q22 + 282q20−371q18 + 283q16−53q14−226q12 + 424q10−463q8 + 336q6−99q4−147q2 + 319−360q−2 + 293q−4−149q−6−q−8 + 105q−10−152q−12 + 134q−14−84q−16 + 37q−18 + 4q−20−22q−22 + 25q−24−20q−26 + 10q−28−4q−30 + q−32 |
Further Quantum Invariants
Further quantum knot invariants for 10_89.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | −q17 + 2q15−4q13 + 5q11−3q9 + 2q7 + q5−3q3 + 4q−4q−1 + 4q−3−q−5 |
| 2 | q48−2q46 + 7q42−11q40−4q38 + 28q36−22q34−24q32 + 52q30−13q28−46q26 + 45q24 + 10q22−41q20 + 10q18 + 26q16−11q14−28q12 + 28q10 + 23q8−51q6 + 13q4 + 46q2−45−9q−2 + 41q−4−18q−6−15q−8 + 16q−10−4q−14 + q−16 |
| 3 | −q93 + 2q91−3q87−q85 + 10q83 + 2q81−26q79−7q77 + 54q75 + 29q73−93q71−85q69 + 132q67 + 173q65−141q63−283q61 + 98q59 + 399q57−15q55−463q53−110q51 + 468q49 + 232q47−410q45−322q43 + 300q41 + 364q39−162q37−366q35 + 23q33 + 335q31 + 108q29−278q27−235q25 + 212q23 + 342q21−125q19−431q17 + 22q15 + 481q13 + 99q11−472q9−220q7 + 412q5 + 305q3−296q−339q−1 + 161q−3 + 316q−5−44q−7−245q−9−27q−11 + 153q−13 + 55q−15−76q−17−52q−19 + 33q−21 + 26q−23−5q−25−12q−27 + 4q−31−q−33 |
| 4 | q152−2q150 + 3q146−3q144 + 2q142−8q140 + 6q138 + 23q136−16q134−22q132−49q130 + 41q128 + 151q126 + 15q124−146q122−324q120−11q118 + 554q116 + 467q114−146q112−1114q110−782q108 + 849q106 + 1711q104 + 901q102−1772q100−2651q98−221q96 + 2762q94 + 3300q92−765q90−4226q88−2817q86 + 1903q84 + 5239q82 + 1857q80−3629q78−4881q76−610q74 + 4849q72 + 3947q70−1251q68−4730q66−2716q64 + 2638q62 + 4147q60 + 1049q58−3021q56−3414q54 + 250q52 + 3176q50 + 2520q48−1089q46−3367q44−1789q42 + 2012q40 + 3655q38 + 828q36−3093q34−3776q32 + 481q30 + 4413q28 + 3046q26−1959q24−5266q22−1814q20 + 3744q18 + 4824q16 + 447q14−4886q12−3842q10 + 1286q8 + 4600q6 + 2754q4−2443q2−3854−1200q−2 + 2355q−4 + 3049q−6 + 33q−8−2001q−10−1792q−12 + 214q−14 + 1649q−16 + 787q−18−325q−20−942q−22−424q−24 + 407q−26 + 404q−28 + 159q−30−217q−32−218q−34 + 20q−36 + 70q−38 + 80q−40−12q−42−41q−44−6q−46 + q−48 + 12q−50−4q−54 + q−56 |
| 5 | −q225 + 2q223−3q219 + 3q217 + 2q215−4q213−3q209−10q207 + 16q205 + 35q203 + 4q201−43q199−87q197−65q195 + 86q193 + 270q191 + 241q189−123q187−596q185−715q183−71q181 + 1086q179 + 1754q177 + 853q175−1496q173−3471q171−2798q169 + 1107q167 + 5650q165 + 6458q163 + 1096q161−7421q159−11722q157−6171q155 + 7094q153 + 17634q151 + 14573q149−2987q147−22168q145−25315q143−5950q141 + 22718q139 + 36151q137 + 19352q135−17569q133−44044q131−34713q129 + 6358q127 + 46080q125 + 48917q123 + 9119q121−41311q119−58405q117−25564q115 + 30330q113 + 61169q111 + 39626q109−15812q107−57053q105−48626q103 + 919q101 + 47596q99 + 51649q97 + 11772q95−35438q93−49490q91−20768q89 + 23129q87 + 43925q85 + 26084q83−12255q81−37181q79−28848q77 + 3427q75 + 30902q73 + 30564q71 + 3847q69−25727q67−32663q65−10767q63 + 21497q61 + 35822q59 + 18379q57−17048q55−39615q53−27604q51 + 11020q49 + 42957q47 + 38068q45−2269q43−43836q41−48586q39−9591q37 + 40532q35 + 57018q33 + 23457q31−31987q29−60809q27−37193q25 + 18594q23 + 58265q21 + 47857q19−2576q17−48963q15−52714q13−12990q11 + 34586q9 + 50561q7 + 24670q5−18247q3−42087q−30233q−1 + 3516q−3 + 29774q−5 + 29448q−7 + 6868q−9−17054q−11−23886q−13−11740q−15 + 6613q−17 + 16218q−19 + 11977q−21 + 54q−23−9063q−25−9378q−27−2951q−29 + 3795q−31 + 5934q−33 + 3362q−35−813q−37−3146q−39−2475q−41−336q−43 + 1258q−45 + 1433q−47 + 592q−49−389q−51−698q−53−372q−55 + 38q−57 + 252q−59 + 202q−61 + 41q−63−88q−65−84q−67−16q−69 + 20q−71 + 21q−73 + 10q−75−q−77−12q−79 + 4q−83−q−85 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | −q26−q24 + 2q22−q20−q18 + 4q16−2q14 + 2q12−2q8 + 2q6−4q4 + 4q2−q−2 + 3q−4−q−6 |
| 2,0 | q66 + q64−q62−3q60 + q58 + 6q56−3q54−12q52 + 18q48 + 3q46−22q44−2q42 + 27q40 + 2q38−27q36 + 21q32−4q30−21q28 + 8q26 + 9q24−11q22 + 8q20 + 9q18−11q16−3q14 + 23q12−q10−28q8 + 4q6 + 28q4−7q2−27 + 11q−2 + 19q−4−6q−6−11q−8 + 2q−10 + 9q−12−2q−14−3q−16 + q−18 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q54−2q52 + q50 + 5q48−10q46 + q44 + 17q42−25q40−q38 + 34q36−35q34−3q32 + 39q30−28q28−7q26 + 26q24−7q22−11q20 + 16q16−5q14−25q12 + 30q10 + 7q8−40q6 + 30q4 + 11q2−34 + 22q−2 + 7q−4−17q−6 + 10q−8 + 2q−10−4q−12 + q−14 |
| 1,0,0 | −q35−q33−q31 + 2q29−q27 + 2q25−q23 + 4q21−3q19 + 3q17−q15−q11−q9 + q7−3q5 + 4q3−q + 3q−1−2q−3 + 3q−5−q−7 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | −q54 + 2q52−5q50 + 9q48−16q46 + 23q44−33q42 + 41q40−45q38 + 46q36−39q34 + 27q32−7q30−14q28 + 39q26−60q24 + 79q22−89q20 + 90q18−84q16 + 67q14−47q12 + 22q10 + q8−22q6 + 38q4−45q2 + 48−44q−2 + 39q−4−27q−6 + 18q−8−10q−10 + 4q−12−q−14 |
| 1,0 | q88−2q84−2q82 + 3q80 + 7q78−13q74−10q72 + 12q70 + 25q68−q66−36q64−21q62 + 30q60 + 42q58−11q56−51q54−13q52 + 45q50 + 31q48−28q46−38q44 + 14q42 + 38q40−q38−35q36−6q34 + 31q32 + 12q30−28q28−20q26 + 25q24 + 27q22−20q20−36q18 + 12q16 + 46q14 + 7q12−47q10−29q8 + 36q6 + 45q4−13q2−46−11q−2 + 33q−4 + 25q−6−15q−8−22q−10 + 14q−14 + 6q−16−4q−18−4q−20 + q−24 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q128−2q126 + 5q124−8q122 + 9q120−9q118 + q116 + 13q114−32q112 + 52q110−67q108 + 62q106−34q104−26q102 + 111q100−190q98 + 234q96−208q94 + 89q92 + 87q90−276q88 + 405q86−402q84 + 261q82−14q80−243q78 + 405q76−399q74 + 229q72 + 28q70−252q68 + 332q66−238q64 + 7q62 + 270q60−447q58 + 447q56−250q54−76q52 + 406q50−617q48 + 623q46−423q44 + 92q42 + 264q40−515q38 + 577q36−433q34 + 148q32 + 148q30−350q28 + 361q26−198q24−53q22 + 282q20−371q18 + 283q16−53q14−226q12 + 424q10−463q8 + 336q6−99q4−147q2 + 319−360q−2 + 293q−4−149q−6−q−8 + 105q−10−152q−12 + 134q−14−84q−16 + 37q−18 + 4q−20−22q−22 + 25q−24−20q−26 + 10q−28−4q−30 + q−32 |
.
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]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
| K = Knot["10 89"];
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In[4]:=
| Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| t3−8t2 + 24t−33 + 24t−1−8t−2 + t−3 |
In[5]:=
| Conway[K][z]
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Out[5]=
| z6−2z4 + z2 + 1 |
In[6]:=
| Alexander[K, 2][t]
|
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.
|
Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
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Out[7]=
| { 99, -2 } |
In[8]:=
| Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
| −q2 + 5q−9 + 13q−1−16q−2 + 17q−3−15q−4 + 12q−5−7q−6 + 3q−7−q−8 |
In[9]:=
| HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| −a8 + 3z2a6 + 2a6−3z4a4−4z2a4−a4 + z6a2 + 2z4a2 + 2z2a2−z4 + 1 |
In[10]:=
| Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| z5a9−2z3a9 + za9 + 3z6a8−5z4a8 + 3z2a8−a8 + 5z7a7−7z5a7 + 4z3a7−za7 + 5z8a6−3z6a6−4z4a6 + 6z2a6−2a6 + 2z9a5 + 11z7a5−27z5a5 + 20z3a5−4za5 + 12z8a4−15z6a4−2z4a4 + 6z2a4−a4 + 2z9a3 + 15z7a3−35z5a3 + 19z3a3−2za3 + 7z8a2−4z6a2−9z4a2 + 3z2a2 + 9z7a−15z5a + 5z3a + 5z6−6z4 + 1 + z5a−1 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, 
):
{}
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]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 89"];
|
In[4]:=
| {A = Alexander[K][t], J = Jones[K][q]}
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[4]=
| { t3−8t2 + 24t−33 + 24t−1−8t−2 + t−3, −q2 + 5q−9 + 13q−1−16q−2 + 17q−3−15q−4 + 12q−5−7q−6 + 3q−7−q−8 } |
In[5]:=
| DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
|
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
|
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
|
Out[5]=
| {} |
In[6]:=
| DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
| {} |
[edit] Vassiliev invariants
| V2 and V3: | (1, -3) |
| 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.
[edit] Khovanov Homology
| The coefficients of the monomials trqj are shown, along with their alternating sums χ (fixed j, alternation over r). The squares with yellow highlighting are those on the "critical diagonals", where j−2r = s + 1 or j−2r = s−1, where s = -2 is the signature of 10 89. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
| Integral Khovanov Homology
(db, data source) |
|
[edit] The Coloured Jones Polynomials
| n | Jn |
| 2 | q7−5q6 + 4q5 + 17q4−36q3 + q2 + 76q−86−35q−1 + 167q−2−119q−3−99q−4 + 241q−5−114q−6−155q−7 + 258q−8−77q−9−171q−10 + 207q−11−26q−12−136q−13 + 116q−14 + 7q−15−71q−16 + 40q−17 + 9q−18−21q−19 + 8q−20 + 2q−21−3q−22 + q−23 |
| 3 | −q15 + 5q14−4q13−12q12 + 6q11 + 36q10 + 3q9−97q8−18q7 + 167q6 + 101q5−277q4−236q3 + 368q2 + 461q−432−736q−1 + 411q−2 + 1062q−3−325q−4−1368q−5 + 159q−6 + 1633q−7 + 57q−8−1827q−9−294q−10 + 1939q−11 + 524q−12−1957q−13−741q−14 + 1896q−15 + 910q−16−1730q−17−1053q−18 + 1507q−19 + 1114q−20−1204q−21−1117q−22 + 885q−23 + 1026q−24−562q−25−881q−26 + 307q−27 + 673q−28−114q−29−467q−30 + 6q−31 + 292q−32 + 28q−33−153q−34−35q−35 + 75q−36 + 20q−37−31q−38−10q−39 + 14q−40 + q−41−3q−42−2q−43 + 3q−44−q−45 |
| 4 | q26−5q25 + 4q24 + 12q23−11q22−6q21−40q20 + 33q19 + 104q18−21q17−56q16−278q15 + 34q14 + 480q13 + 224q12−53q11−1109q10−484q9 + 1097q8 + 1336q7 + 809q6−2544q5−2490q4 + 888q3 + 3370q2 + 3825q−3238−6045q−1−1766q−2 + 4781q−3 + 9022q−4−1392q−5−9359q−6−6894q−7 + 3737q−8 + 14355q−9 + 2985q−10−10439q−11−12452q−12 + 285q−13 + 17662q−14 + 7990q−15−9072q−16−16384q−17−3972q−18 + 18345q−19 + 11911q−20−6245q−21−18027q−22−7773q−23 + 16767q−24 + 14189q−25−2636q−26−17371q−27−10699q−28 + 13103q−29 + 14582q−30 + 1434q−31−14273q−32−12208q−33 + 7749q−34 + 12568q−35 + 4913q−36−9075q−37−11306q−38 + 2290q−39 + 8297q−40 + 6165q−41−3589q−42−7924q−43−1046q−44 + 3577q−45 + 4756q−46−128q−47−3859q−48−1584q−49 + 594q−50 + 2326q−51 + 751q−52−1186q−53−774q−54−268q−55 + 695q−56 + 419q−57−218q−58−161q−59−181q−60 + 130q−61 + 106q−62−40q−63−45q−65 + 20q−66 + 16q−67−13q−68 + 6q−69−6q−70 + 3q−71 + 2q−72−3q−73 + q−74 |
| 5 | −q40 + 5q39−4q38−12q37 + 11q36 + 11q35 + 10q34 + 4q33−40q32−80q31 + 7q30 + 140q29 + 171q28 + 54q27−254q26−490q25−319q24 + 449q23 + 1152q22 + 895q21−429q20−2084q19−2458q18−222q17 + 3485q16 + 5070q15 + 2143q14−4223q13−9204q12−6649q11 + 3800q10 + 14187q9 + 14066q8 + 18q7−18809q6−25002q5−8346q4 + 21019q3 + 37988q2 + 22598q−18483−51260q−1−42095q−2 + 9165q−3 + 61828q−4 + 65515q−5 + 7408q−6−67235q−7−89671q−8−30559q−9 + 65579q−10 + 111902q−11 + 57841q−12−56827q−13−129342q−14−86346q−15 + 41963q−16 + 140724q−17 + 113285q−18−23266q−19−145828q−20−136469q−21 + 2968q−22 + 145474q−23 + 154852q−24 + 17071q−25−140939q−26−168406q−27−35656q−28 + 133463q−29 + 177419q−30 + 52498q−31−123496q−32−182731q−33−67920q−34 + 111567q−35 + 184355q−36 + 82072q−37−96779q−38−182393q−39−95395q−40 + 79292q−41 + 176022q−42 + 106998q−43−58440q−44−164552q−45−116191q−46 + 35395q−47 + 147300q−48 + 121050q−49−11230q−50−124675q−51−120244q−52−11282q−53 + 97755q−54 + 112623q−55 + 30011q−56−69237q−57−98701q−58−42121q−59 + 41861q−60 + 79782q−61 + 47105q−62−18807q−63−58903q−64−44958q−65 + 2139q−66 + 38711q−67 + 37774q−68 + 7668q−69−21982q−70−28159q−71−11294q−72 + 10043q−73 + 18409q−74 + 10815q−75−2801q−76−10599q−77−8233q−78−497q−79 + 5144q−80 + 5264q−81 + 1500q−82−2082q−83−2871q−84−1305q−85 + 601q−86 + 1359q−87 + 827q−88−107q−89−522q−90−404q−91−67q−92 + 202q−93 + 183q−94 + 12q−95−49q−96−40q−97−38q−98 + 18q−99 + 32q−100−10q−101−5q−102 + 7q−103−7q−104−q−105 + 6q−106−3q−107−2q−108 + 3q−109−q−110 |
| 6 | q57−5q56 + 4q55 + 12q54−11q53−11q52−15q51 + 26q50 + 3q49 + 16q48 + 94q47−76q46−130q45−166q44 + 70q43 + 159q42 + 285q41 + 592q40−162q39−786q38−1315q37−492q36 + 358q35 + 1823q34 + 3589q33 + 1467q32−1862q31−6117q30−5872q29−3275q28 + 4221q27 + 14196q26 + 13763q25 + 4612q24−13711q23−25068q22−27520q21−7712q20 + 29398q19 + 52006q18 + 47384q17 + 2707q16−50689q15−95331q14−79513q13 + 4575q12 + 101533q11 + 157541q10 + 110029q9−14670q8−179840q7−249195q6−151498q5 + 65923q4 + 290494q3 + 350261q2 + 197545q−153211−449328q−1−478721q−2−188657q−3 + 287272q−4 + 629512q−5 + 615513q−6 + 130178q−7−493832q−8−853697q−9−674173q−10 + 85q−11 + 741503q−12 + 1085958q−13 + 658679q−14−241986q−15−1056845q−16−1211702q−17−533358q−18 + 559209q−19 + 1383990q−20 + 1234571q−21 + 245365q−22−976920q−23−1580502q−24−1106663q−25 + 159076q−26 + 1414442q−27 + 1649785q−28 + 766439q−29−695670q−30−1702203q−31−1533185q−32−274757q−33 + 1256130q−34 + 1843110q−35 + 1164970q−36−369544q−37−1649075q−38−1770803q−39−622190q−40 + 1033995q−41 + 1879600q−42 + 1420734q−43−80945q−44−1516518q−45−1879548q−46−885422q−47 + 795906q−48 + 1828892q−49 + 1591422q−50 + 192914q−51−1322990q−52−1907246q−53−1120225q−54 + 502100q−55 + 1683461q−56 + 1704725q−57 + 504094q−58−1014325q−59−1821200q−60−1332607q−61 + 107102q−62 + 1374897q−63 + 1700374q−64 + 832731q−65−553067q−66−1536799q−67−1430264q−68−339098q−69 + 873701q−70 + 1474204q−71 + 1049771q−72−20239q−73−1031393q−74−1287386q−75−669820q−76 + 290363q−77 + 1009106q−78 + 1008702q−79 + 385642q−80−441190q−81−893256q−82−724847q−83−154155q−84 + 461572q−85 + 708363q−86 + 503434q−87 + 1901q−88−419792q−89−518360q−90−309994q−91 + 61894q−92 + 330955q−93 + 368560q−94 + 169279q−95−85271q−96−237747q−97−234071q−98−89280q−99 + 74382q−100 + 167164q−101 + 135206q−102 + 38741q−103−54925q−104−101709q−105−76580q−106−16054q−107 + 41676q−108 + 55570q−109 + 37906q−110 + 5490q−111−23995q−112−30296q−113−18510q−114 + 1825q−115 + 11931q−116 + 13858q−117 + 8319q−118−1409q−119−6551q−120−6486q−121−1947q−122 + 633q−123 + 2561q−124 + 2778q−125 + 757q−126−723q−127−1264q−128−474q−129−299q−130 + 163q−131 + 538q−132 + 222q−133−39q−134−183q−135 + 6q−136−80q−137−39q−138 + 84q−139 + 29q−140−2q−141−35q−142 + 23q−143−5q−144−18q−145 + 13q−146 + 2q−147 + q−148−6q−149 + 3q−150 + 2q−151−3q−152 + q−153 |
[edit] 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.
[edit] 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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