10 59
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 59's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_59's page at Knotilus! Visit 10 59's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X4251 X10,6,11,5 X8394 X2,9,3,10 X14,8,15,7 X18,12,19,11 X20,15,1,16 X16,19,17,20 X12,18,13,17 X6,14,7,13 |
| Gauss code | 1, -4, 3, -1, 2, -10, 5, -3, 4, -2, 6, -9, 10, -5, 7, -8, 9, -6, 8, -7 |
| Dowker-Thistlethwaite code | 4 8 10 14 2 18 6 20 12 16 |
| Conway Notation | [22,211,2] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 | 
|  [{9, 12}, {11, 3}, {12, 10}, {7, 11}, {6, 8}, {5, 7}, {4, 2}, {3, 6}, {1, 4}, {2, 9}, {8, 1}, {10, 5}] |
[edit Notes on presentations of 10 59]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["10 59"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X4251 X10,6,11,5 X8394 X2,9,3,10 X14,8,15,7 X18,12,19,11 X20,15,1,16 X16,19,17,20 X12,18,13,17 X6,14,7,13 |
In[5]:=
| GaussCode[K]
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Out[5]=
| 1, -4, 3, -1, 2, -10, 5, -3, 4, -2, 6, -9, 10, -5, 7, -8, 9, -6, 8, -7 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 8 10 14 2 18 6 20 12 16 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [22,211,2] |
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,−3,2,2,4,−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, 10, 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[{9, 12}, {11, 3}, {12, 10}, {7, 11}, {6, 8}, {5, 7}, {4, 2}, {3, 6}, {1, 4}, {2, 9}, {8, 1}, {10, 5}] |
In[14]:=
| Draw[ap]
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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 | t3−7t2 + 18t−23 + 18t−1−7t−2 + t−3 |
| Conway polynomial | z6−z4−z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 75, 2 } |
| Jones polynomial | q7−3q6 + 6q5−10q4 + 12q3−12q2 + 12q−9 + 6q−1−3q−2 + q−3 |
| HOMFLY-PT polynomial (db, data sources) | z6a−2 + 3z4a−2−2z4a−4−2z4 + a2z2 + 5z2a−2−4z2a−4 + z2a−6−4z2 + a2 + 4a−2−3a−4 + a−6−2 |
| Kauffman polynomial (db, data sources) | z9a−1 + z9a−3 + 7z8a−2 + 4z8a−4 + 3z8 + 3az7 + 8z7a−1 + 11z7a−3 + 6z7a−5 + a2z6−9z6a−2 + z6a−4 + 5z6a−6−4z6−9az5−27z5a−1−28z5a−3−7z5a−5 + 3z5a−7−3a2z4−8z4a−2−11z4a−4−5z4a−6 + z4a−8−6z4 + 8az3 + 21z3a−1 + 20z3a−3 + 4z3a−5−3z3a−7 + 3a2z2 + 11z2a−2 + 10z2a−4 + 3z2a−6−z2a−8 + 8z2−2az−5za−1−4za−3 + za−7−a2−4a−2−3a−4−a−6−2 |
| The A2 invariant | q10−q6 + 2q4−2q2 + 2q−2−q−4 + 4q−6−q−8 + q−10−q−12−3q−14 + 2q−16−q−18 + q−22 |
| The G2 invariant | q46−2q44 + 6q42−10q40 + 12q38−10q36−q34 + 23q32−44q30 + 64q28−63q26 + 33q24 + 18q22−83q20 + 135q18−149q16 + 112q14−28q12−76q10 + 158q8−183q6 + 145q4−55q2−52 + 123q−2−140q−4 + 86q−6 + 9q−8−96q−10 + 143q−12−111q−14 + 24q−16 + 88q−18−182q−20 + 220q−22−177q−24 + 68q−26 + 74q−28−192q−30 + 256q−32−225q−34 + 126q−36 + 6q−38−123q−40 + 179q−42−167q−44 + 85q−46 + 20q−48−97q−50 + 117q−52−74q−54−17q−56 + 101q−58−146q−60 + 127q−62−63q−64−31q−66 + 113q−68−154q−70 + 149q−72−93q−74 + 23q−76 + 41q−78−84q−80 + 92q−82−79q−84 + 52q−86−16q−88−10q−90 + 27q−92−32q−94 + 28q−96−19q−98 + 11q−100−2q−102−4q−104 + 5q−106−6q−108 + 4q−110−2q−112 + q−114 |
Further Quantum Invariants
Further quantum knot invariants for 10_59.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q7−2q5 + 3q3−3q + 3q−1 + 2q−7−4q−9 + 3q−11−2q−13 + q−15 |
| 2 | q22−2q20−2q18 + 8q16−3q14−12q12 + 17q10 + 4q8−26q6 + 15q4 + 17q2−27 + 4q−2 + 22q−4−14q−6−9q−8 + 14q−10 + 6q−12−16q−14−3q−16 + 24q−18−15q−20−18q−22 + 29q−24−5q−26−19q−28 + 17q−30 + q−32−9q−34 + 5q−36−2q−40 + q−42 |
| 3 | q45−2q43−2q41 + 3q39 + 8q37−3q35−19q33−q31 + 32q29 + 16q27−45q25−44q23 + 50q21 + 79q19−35q17−115q15 + 3q13 + 142q11 + 42q9−147q7−91q5 + 129q3 + 134q−102q−1−154q−3 + 61q−5 + 165q−7−19q−9−156q−11−18q−13 + 137q−15 + 54q−17−106q−19−87q−21 + 62q−23 + 119q−25−17q−27−137q−29−42q−31 + 145q−33 + 91q−35−128q−37−134q−39 + 103q−41 + 152q−43−64q−45−143q−47 + 23q−49 + 121q−51−q−53−85q−55−11q−57 + 51q−59 + 12q−61−27q−63−8q−65 + 14q−67 + 2q−69−5q−71 + 2q−75−2q−79 + q−81 |
| 4 | q76−2q74−2q72 + 3q70 + 3q68 + 8q66−10q64−19q62−q60 + 14q58 + 53q56−q54−67q52−64q50−13q48 + 157q46 + 117q44−58q42−213q40−229q38 + 174q36 + 366q34 + 219q32−227q30−624q28−168q26 + 432q24 + 724q22 + 204q20−792q18−775q16−15q14 + 977q12 + 909q10−399q8−1123q6−743q4 + 676q2 + 1331 + 282q−2−940q−4−1202q−6 + 105q−8 + 1243q−10 + 766q−12−499q−14−1218q−16−332q−18 + 871q−20 + 921q−22−84q−24−976q−26−609q−28 + 410q−30 + 928q−32 + 334q−34−601q−36−855q−38−183q−40 + 800q−42 + 823q−44 + 3q−46−971q−48−901q−50 + 374q−52 + 1141q−54 + 764q−56−682q−58−1373q−60−296q−62 + 941q−64 + 1238q−66−68q−68−1213q−70−735q−72 + 345q−74 + 1079q−76 + 379q−78−622q−80−646q−82−105q−84 + 558q−86 + 371q−88−157q−90−293q−92−175q−94 + 169q−96 + 168q−98−8q−100−65q−102−83q−104 + 34q−106 + 40q−108−2q−110−21q−114 + 7q−116 + 5q−118−4q−120 + 4q−122−3q−124 + 2q−126−2q−130 + q−132 |
| 5 | q115−2q113−2q111 + 3q109 + 3q107 + 3q105 + q103−10q101−19q99−q97 + 23q95 + 35q93 + 27q91−23q89−85q87−89q85 + 9q83 + 138q81 + 196q79 + 96q77−158q75−378q73−322q71 + 72q69 + 543q67 + 695q65 + 268q63−568q61−1177q59−914q57 + 266q55 + 1540q53 + 1828q51 + 587q49−1513q47−2818q45−1968q43 + 793q41 + 3448q39 + 3691q37 + 794q35−3334q33−5328q31−3066q29 + 2184q27 + 6311q25 + 5617q23 + 15q21−6259q19−7859q17−2875q15 + 5033q13 + 9235q11 + 5829q9−2791q7−9491q5−8329q3 + 86q + 8648q−1 + 9869q−3 + 2601q−5−6974q−7−10438q−9−4742q−11 + 4983q−13 + 10058q−15 + 6127q−17−3010q−19−9090q−21−6793q−23 + 1407q−25 + 7849q−27 + 6891q−29−169q−31−6607q−33−6724q−35−809q−37 + 5491q−39 + 6538q−41 + 1725q−43−4415q−45−6478q−47−2842q−49 + 3226q−51 + 6503q−53 + 4267q−55−1664q−57−6445q−59−5982q−61−366q−63 + 5954q−65 + 7714q−67 + 2969q−69−4836q−71−9102q−73−5758q−75 + 2879q−77 + 9654q−79 + 8445q−81−279q−83−9174q−85−10342q−87−2584q−89 + 7509q−91 + 11130q−93 + 5151q−95−5068q−97−10600q−99−6856q−101 + 2367q−103 + 8890q−105 + 7465q−107 + 29q−109−6579q−111−6955q−113−1623q−115 + 4154q−117 + 5651q−119 + 2375q−121−2159q−123−4050q−125−2356q−127 + 802q−129 + 2556q−131 + 1882q−133−61q−135−1413q−137−1291q−139−223q−141 + 697q−143 + 767q−145 + 230q−147−284q−149−397q−151−173q−153 + 101q−155 + 194q−157 + 89q−159−34q−161−73q−163−41q−165 + 4q−167 + 27q−169 + 22q−171−5q−173−12q−175−2q−179−q−181 + 5q−183 + q−185−3q−187 + 2q−189−2q−193 + q−195 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q10−q6 + 2q4−2q2 + 2q−2−q−4 + 4q−6−q−8 + q−10−q−12−3q−14 + 2q−16−q−18 + q−22 |
| 2,0 | q28−2q24−2q22 + 3q20 + 5q18−4q16−6q14 + 6q12 + 9q10−6q8−11q6 + 7q4 + 12q2−9−9q−2 + 11q−4 + 3q−6−7q−8 + 7q−12−2q−14 + 10q−18−3q−20−12q−22 + 5q−24 + 8q−26−15q−28−8q−30 + 13q−32 + 8q−34−8q−36−4q−38 + 10q−40 + 3q−42−6q−44−2q−46 + q−48−q−52 + q−56 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q20−2q18 + 2q16 + 3q14−8q12 + 7q10 + 5q8−16q6 + 13q4 + 6q2−21 + 14q−2 + 9q−4−18q−6 + 8q−8 + 11q−10−5q−12−4q−14 + 3q−16 + 7q−18−13q−20−7q−22 + 20q−24−13q−26−10q−28 + 24q−30−9q−32−10q−34 + 15q−36−3q−38−7q−40 + 5q−42−2q−46 + q−48 |
| 1,0,0 | q13 + q9−q7 + 2q5−3q3 + q−2q−1 + 2q−3 + 3q−7 + 3q−9 + q−13−3q−15−4q−19 + 2q−21−q−23 + q−25 + q−29 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | q20−2q18 + 6q16−9q14 + 14q12−19q10 + 23q8−26q6 + 25q4−22q2 + 13−4q−2−7q−4 + 22q−6−32q−8 + 45q−10−47q−12 + 50q−14−45q−16 + 37q−18−27q−20 + 13q−22−2q−24−11q−26 + 18q−28−24q−30 + 25q−32−24q−34 + 21q−36−15q−38 + 11q−40−7q−42 + 4q−44−2q−46 + q−48 |
| 1,0 | q34−2q30−2q28 + 4q26 + 6q24−3q22−11q20−3q18 + 15q16 + 13q14−12q12−22q10 + 2q8 + 27q6 + 12q4−23q2−22 + 11q−2 + 26q−4 + 2q−6−23q−8−8q−10 + 17q−12 + 13q−14−12q−16−11q−18 + 10q−20 + 15q−22−7q−24−18q−26 + 2q−28 + 19q−30 + 2q−32−22q−34−11q−36 + 19q−38 + 19q−40−13q−42−25q−44 + 2q−46 + 27q−48 + 11q−50−17q−52−19q−54 + 5q−56 + 18q−58 + 5q−60−9q−62−9q−64 + q−66 + 6q−68 + 2q−70−2q−72−2q−74 + q−78 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q46−2q44 + 6q42−10q40 + 12q38−10q36−q34 + 23q32−44q30 + 64q28−63q26 + 33q24 + 18q22−83q20 + 135q18−149q16 + 112q14−28q12−76q10 + 158q8−183q6 + 145q4−55q2−52 + 123q−2−140q−4 + 86q−6 + 9q−8−96q−10 + 143q−12−111q−14 + 24q−16 + 88q−18−182q−20 + 220q−22−177q−24 + 68q−26 + 74q−28−192q−30 + 256q−32−225q−34 + 126q−36 + 6q−38−123q−40 + 179q−42−167q−44 + 85q−46 + 20q−48−97q−50 + 117q−52−74q−54−17q−56 + 101q−58−146q−60 + 127q−62−63q−64−31q−66 + 113q−68−154q−70 + 149q−72−93q−74 + 23q−76 + 41q−78−84q−80 + 92q−82−79q−84 + 52q−86−16q−88−10q−90 + 27q−92−32q−94 + 28q−96−19q−98 + 11q−100−2q−102−4q−104 + 5q−106−6q−108 + 4q−110−2q−112 + q−114 |
.
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 59"];
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In[4]:=
| Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| t3−7t2 + 18t−23 + 18t−1−7t−2 + t−3 |
In[5]:=
| Conway[K][z]
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Out[5]=
| z6−z4−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]=
| { 75, 2 } |
In[8]:=
| Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
| q7−3q6 + 6q5−10q4 + 12q3−12q2 + 12q−9 + 6q−1−3q−2 + q−3 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| z6a−2 + 3z4a−2−2z4a−4−2z4 + a2z2 + 5z2a−2−4z2a−4 + z2a−6−4z2 + a2 + 4a−2−3a−4 + a−6−2 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| z9a−1 + z9a−3 + 7z8a−2 + 4z8a−4 + 3z8 + 3az7 + 8z7a−1 + 11z7a−3 + 6z7a−5 + a2z6−9z6a−2 + z6a−4 + 5z6a−6−4z6−9az5−27z5a−1−28z5a−3−7z5a−5 + 3z5a−7−3a2z4−8z4a−2−11z4a−4−5z4a−6 + z4a−8−6z4 + 8az3 + 21z3a−1 + 20z3a−3 + 4z3a−5−3z3a−7 + 3a2z2 + 11z2a−2 + 10z2a−4 + 3z2a−6−z2a−8 + 8z2−2az−5za−1−4za−3 + za−7−a2−4a−2−3a−4−a−6−2 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {9_40, K11n66,}
Same Jones Polynomial (up to mirroring, 
):
{10_106,}
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 59"];
|
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]=
| { t3−7t2 + 18t−23 + 18t−1−7t−2 + t−3, q7−3q6 + 6q5−10q4 + 12q3−12q2 + 12q−9 + 6q−1−3q−2 + q−3 } |
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]=
| {9_40, K11n66,} |
In[6]:=
| DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
| {10_106,} |
[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 59. 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 | q20−3q19 + 2q18 + 6q17−17q16 + 12q15 + 22q14−53q13 + 26q12 + 56q11−100q10 + 29q9 + 95q8−127q7 + 16q6 + 117q5−119q4−7q3 + 112q2−83q−25 + 81q−1−39q−2−27q−3 + 40q−4−9q−5−14q−6 + 11q−7−3q−9 + q−10 |
| 3 | q39−3q38 + 2q37 + 2q36−q35−8q34 + 9q33 + 14q32−23q31−27q30 + 48q29 + 53q28−85q27−101q26 + 132q25 + 175q24−183q23−267q22 + 211q21 + 391q20−232q19−504q18 + 217q17 + 610q16−178q15−691q14 + 122q13 + 730q12−42q11−748q10−27q9 + 711q8 + 118q7−665q6−182q5 + 573q4 + 255q3−481q2−286q + 358 + 307q−1−245q−2−291q−3 + 138q−4 + 251q−5−56q−6−191q−7−q−8 + 133q−9 + 24q−10−77q−11−30q−12 + 39q−13 + 23q−14−16q−15−14q−16 + 6q−17 + 5q−18−3q−20 + q−21 |
| 4 | q64−3q63 + 2q62 + 2q61−5q60 + 8q59−11q58 + 11q57 + 4q56−33q55 + 29q54−13q53 + 53q52−2q51−150q50 + 47q49 + 44q48 + 229q47−q46−494q45−71q44 + 180q43 + 757q42 + 186q41−1157q40−612q39 + 204q38 + 1758q37 + 886q36−1891q35−1692q34−274q33 + 2903q32 + 2192q31−2188q30−2929q29−1351q28 + 3594q27 + 3638q26−1811q25−3696q24−2626q23 + 3524q22 + 4612q21−991q20−3719q19−3609q18 + 2852q17 + 4866q16−56q15−3125q14−4127q13 + 1833q12 + 4499q11 + 836q10−2120q9−4177q8 + 630q7 + 3613q6 + 1555q5−855q4−3700q3−508q2 + 2306q + 1817 + 367q−1−2651q−2−1163q−3 + 887q−4 + 1437q−5 + 1091q−6−1343q−7−1095q−8−105q−9 + 677q−10 + 1074q−11−347q−12−575q−13−397q−14 + 77q−15 + 618q−16 + 50q−17−129q−18−250q−19−115q−20 + 215q−21 + 66q−22 + 26q−23−75q−24−75q−25 + 45q−26 + 15q−27 + 23q−28−9q−29−21q−30 + 6q−31 + 5q−33−3q−35 + q−36 |
| 5 | q95−3q94 + 2q93 + 2q92−5q91 + 4q90 + 5q89−9q88 + q87 + 4q86−17q85 + 11q84 + 32q83−4q82−22q81−41q80−49q79 + 50q78 + 155q77 + 101q76−115q75−315q74−273q73 + 163q72 + 669q71 + 638q70−185q69−1235q68−1341q67 + 41q66 + 2021q65 + 2581q64 + 489q63−2989q62−4499q61−1653q60 + 3912q59 + 7115q58 + 3765q57−4486q56−10276q55−6985q54 + 4288q53 + 13723q52 + 11201q51−3061q50−16799q49−16208q48 + 544q47 + 19255q46 + 21420q45 + 2918q44−20420q43−26301q42−7214q41 + 20423q40 + 30315q39 + 11642q38−19211q37−33076q36−15851q35 + 17079q34 + 34581q33 + 19447q32−14466q31−34836q30−22171q29 + 11463q28 + 34118q27 + 24228q26−8535q25−32600q24−25448q23 + 5395q22 + 30482q21 + 26291q20−2395q19−27787q18−26495q17−905q16 + 24567q15 + 26408q14 + 4043q13−20727q12−25537q11−7347q10 + 16367q9 + 24111q8 + 10123q7−11590q6−21606q5−12422q4 + 6642q3 + 18415q2 + 13587q−2015−14338q−1−13643q−2−1920q−3 + 10000q−4 + 12425q−5 + 4685q−6−5718q−7−10237q−8−6122q−9 + 2092q−10 + 7441q−11 + 6285q−12 + 556q−13−4635q−14−5428q−15−2035q−16 + 2191q−17 + 4023q−18 + 2550q−19−507q−20−2531q−21−2278q−22−464q−23 + 1262q−24 + 1700q−25 + 798q−26−431q−27−1037q−28−752q−29−12q−30 + 520q−31 + 535q−32 + 178q−33−201q−34−325q−35−164q−36 + 49q−37 + 141q−38 + 122q−39 + 19q−40−71q−41−64q−42−9q−43 + 12q−44 + 24q−45 + 23q−46−9q−47−14q−48−q−49 + 5q−52−3q−54 + q−55 |
| 6 | q132−3q131 + 2q130 + 2q129−5q128 + 4q127 + q126 + 7q125−19q124 + q123 + 20q122−25q121 + 16q120 + 18q119 + 21q118−73q117−31q116 + 64q115−44q114 + 82q113 + 112q112 + 42q111−292q110−247q109 + 90q108 + 21q107 + 497q106 + 606q105 + 152q104−1059q103−1376q102−425q101 + 220q100 + 2204q99 + 2916q98 + 1258q97−2865q96−5443q95−3951q94−726q93 + 6525q92 + 10723q91 + 7429q90−4175q89−15120q88−16463q87−8829q86 + 11686q85 + 28398q84 + 27511q83 + 3240q82−28283q81−44153q80−35885q79 + 6963q78 + 53013q77 + 69038q76 + 33878q75−31299q74−82485q73−89733q72−24463q71 + 67566q70 + 124650q69 + 94827q68−5378q67−110736q66−159124q65−88087q64 + 51617q63 + 169514q62 + 170878q61 + 53259q60−107320q59−215770q58−165370q57 + 2969q56 + 181264q55 + 232043q54 + 124295q53−71352q52−237847q51−226639q50−57865q49 + 159895q48 + 258830q47 + 180526q46−22299q45−226671q44−255929q43−107466q42 + 122916q41 + 254329q40 + 210290q39 + 20838q38−197919q37−258084q36−138340q35 + 85001q34 + 232503q33 + 219810q32 + 54199q31−162683q30−245235q29−157373q28 + 47338q27 + 201336q26 + 218957q25 + 84517q24−120303q23−222151q22−171612q21 + 4097q20 + 158404q19 + 208727q18 + 115433q17−65976q16−183941q15−177651q14−44691q13 + 99222q12 + 180816q11 + 138738q10−2953q9−125398q8−163229q7−86074q6 + 29317q5 + 128622q4 + 138288q3 + 51737q2−53665q−120386−100518q−1−31211q−2 + 60715q−3 + 105510q−4 + 76269q−5 + 8646q−6−59455q−7−79642q−8−59587q−9 + 1761q−10 + 53025q−11 + 63614q−12 + 38668q−13−6747q−14−38361q−15−51131q−16−26219q−17 + 8138q−18 + 31017q−19 + 34299q−20 + 17373q−21−3803q−22−24902q−23−23742q−24−11308q−25 + 4420q−26 + 15214q−27 + 15812q−28 + 9456q−29−4507q−30−9950q−31−10160q−32−5012q−33 + 1515q−34 + 6152q−35 + 7515q−36 + 2307q−37−919q−38−3667q−39−3731q−40−2189q−41 + 469q−42 + 2720q−43 + 1729q−44 + 1151q−45−279q−46−1025q−47−1360q−48−625q−49 + 458q−50 + 384q−51 + 612q−52 + 269q−53−387q−55−305q−56 + 13q−57−27q−58 + 134q−59 + 108q−60 + 88q−61−67q−62−71q−63 + 2q−64−33q−65 + 12q−66 + 15q−67 + 32q−68−9q−69−14q−70 + 6q−71−7q−72 + 5q−75−3q−77 + q−78 |
| 7 | q175−3q174 + 2q173 + 2q172−5q171 + 4q170 + q169 + 3q168−3q167−19q166 + 17q165 + 12q164−20q163 + 12q162 + 3q161 + 13q160−18q159−78q158 + 56q157 + 67q156−14q155 + 39q154−35q153−21q152−111q151−247q150 + 152q149 + 325q148 + 266q147 + 262q146−232q145−506q144−785q143−920q142 + 363q141 + 1475q140 + 2037q139 + 1839q138−467q137−2745q136−4522q135−4567q134−245q133 + 5220q132 + 9665q131 + 10101q130 + 2561q129−8323q128−18334q127−21216q126−9528q125 + 10914q124 + 32221q123 + 41491q122 + 25211q121−10127q120−51064q119−74442q118−56212q117−608q116 + 72262q115 + 123499q114 + 110369q113 + 30341q112−89468q111−187950q110−194369q109−91202q108 + 90580q107 + 262071q106 + 312183q105 + 195053q104−60419q103−333639q102−459859q101−349449q100−17771q99 + 383829q98 + 625054q97 + 554478q96 + 156798q95−391708q94−787693q93−798981q92−360028q91 + 339456q90 + 921759q89 + 1060754q88 + 620370q87−216558q86−1004231q85−1313097q84−916642q83 + 27372q82 + 1017968q81 + 1525433q80 + 1221199q79 + 214803q78−959249q77−1677609q76−1503543q75−482798q74 + 836629q73 + 1756491q72 + 1737910q71 + 750054q70−668316q69−1765174q68−1909362q67−990367q66 + 478970q65 + 1715130q64 + 2013147q63 + 1186804q62−290062q61−1624327q60−2057064q59−1333116q58 + 119079q57 + 1512667q56 + 2053620q55 + 1430994q54 + 26504q53−1393841q52−2018872q51−1491657q50−146548q49 + 1278259q48 + 1966185q47 + 1525924q46 + 247682q45−1165838q44−1904384q43−1547603q42−339934q41 + 1054432q40 + 1836659q39 + 1563270q38 + 433405q37−934402q36−1760650q35−1578328q34−535662q33 + 799050q32 + 1669468q31 + 1588648q30 + 650127q29−638978q28−1554650q27−1589201q26−773601q25 + 452900q24 + 1406920q23 + 1566532q22 + 898023q21−240689q20−1220620q19−1510509q18−1009004q17 + 13846q16 + 994613q15 + 1407490q14 + 1089286q13 + 214501q12−735297q11−1253458q10−1122016q9−421402q8 + 458102q7 + 1047594q6 + 1093289q5 + 586349q4−183526q3−802844q2−999366q−688534−61652q−1 + 538408q−2 + 844839q−3 + 717559q−4 + 254425q−5−281280q−6−648043q−7−673235q−8−376793q−9 + 58547q−10 + 434006q−11 + 568182q−12 + 423484q−13 + 108117q−14−231142q−15−425527q−16−402092q−17−207529q−18 + 64525q−19 + 272883q−20 + 330682q−21 + 241488q−22 + 51003q−23−135388q−24−234540q−25−223883q−26−111853q−27 + 31530q−28 + 137589q−29 + 174030q−30 + 126180q−31 + 32687q−32−57695q−33−113998q−34−109320q−35−59734q−36 + 4273q−37 + 59446q−38 + 77364q−39 + 60427q−40 + 23421q−41−19957q−42−44848q−43−46742q−44−30772q−45−2624q−46 + 19304q−47 + 29060q−48 + 26577q−49 + 11643q−50−3586q−51−14239q−52−18098q−53−12038q−54−3445q−55 + 4502q−56 + 9813q−57 + 8779q−58 + 5232q−59 + 428q−60−4316q−61−5140q−62−4126q−63−1847q−64 + 1118q−65 + 2202q−66 + 2606q−67 + 1934q−68 + 94q−69−822q−70−1286q−71−1165q−72−354q−73−12q−74 + 464q−75 + 739q−76 + 340q−77 + 92q−78−184q−79−290q−80−119q−81−142q−82−34q−83 + 142q−84 + 103q−85 + 74q−86−9q−87−56q−88 + 6q−89−33q−90−33q−91 + 12q−92 + 15q−93 + 23q−94−14q−96 + 6q−97−7q−99 + 5q−102−3q−104 + q−105 |
[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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