10 70
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 70's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_70's page at Knotilus! Visit 10 70's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X1425 X7,10,8,11 X3948 X9,3,10,2 X5,16,6,17 X11,19,12,18 X13,1,14,20 X19,13,20,12 X17,15,18,14 X15,6,16,7 |
| Gauss code | -1, 4, -3, 1, -5, 10, -2, 3, -4, 2, -6, 8, -7, 9, -10, 5, -9, 6, -8, 7 |
| Dowker-Thistlethwaite code | 4 8 16 10 2 18 20 6 14 12 |
| Conway Notation | [22,3,2+] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 | 
|  [{13, 10}, {11, 9}, {10, 12}, {3, 11}, {8, 4}, {9, 7}, {5, 8}, {7, 13}, {4, 6}, {2, 5}, {1, 3}, {12, 2}, {6, 1}] |
[edit Notes on presentations of 10 70]
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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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["10 70"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X1425 X7,10,8,11 X3948 X9,3,10,2 X5,16,6,17 X11,19,12,18 X13,1,14,20 X19,13,20,12 X17,15,18,14 X15,6,16,7 |
In[5]:=
| GaussCode[K]
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Out[5]=
| -1, 4, -3, 1, -5, 10, -2, 3, -4, 2, -6, 8, -7, 9, -10, 5, -9, 6, -8, 7 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 8 16 10 2 18 20 6 14 12 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [22,3,2+] |
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,−3,2,2,2,4,−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[{13, 10}, {11, 9}, {10, 12}, {3, 11}, {8, 4}, {9, 7}, {5, 8}, {7, 13}, {4, 6}, {2, 5}, {1, 3}, {12, 2}, {6, 1}] |
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 + 16t−19 + 16t−1−7t−2 + t−3 |
| Conway polynomial | z6−z4−3z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 67, 2 } |
| Jones polynomial | q7−3q6 + 6q5−9q4 + 11q3−11q2 + 10q−8 + 5q−1−2q−2 + q−3 |
| HOMFLY-PT polynomial (db, data sources) | z6a−2 + 3z4a−2−2z4a−4−2z4 + a2z2 + 4z2a−2−4z2a−4 + z2a−6−5z2 + 2a2 + 3a−2−2a−4 + a−6−3 |
| Kauffman polynomial (db, data sources) | z9a−1 + z9a−3 + 5z8a−2 + 3z8a−4 + 2z8 + 2az7 + 3z7a−1 + 6z7a−3 + 5z7a−5 + a2z6−5z6a−2 + 3z6a−4 + 5z6a−6−2z6−6az5−10z5a−1−11z5a−3−4z5a−5 + 3z5a−7−4a2z4−8z4a−2−12z4a−4−6z4a−6 + z4a−8−7z4 + 5az3 + 4z3a−1 + 2z3a−3−3z3a−7 + 5a2z2 + 9z2a−2 + 9z2a−4 + 4z2a−6−z2a−8 + 10z2−az + za−3 + za−5 + za−7−2a2−3a−2−2a−4−a−6−3 |
| The A2 invariant | q10 + q8 + 2q4−2q2−1 + q−2−2q−4 + 3q−6−q−8 + q−10−2q−14 + 2q−16−q−18 + q−22 |
| The G2 invariant | q46−q44 + 4q42−5q40 + 6q38−5q36 + 12q32−23q30 + 36q28−37q26 + 25q24 + 5q22−42q20 + 80q18−97q16 + 85q14−40q12−32q10 + 96q8−132q6 + 124q4−70q2−6 + 70q−2−108q−4 + 90q−6−38q−8−31q−10 + 81q−12−86q−14 + 46q−16 + 27q−18−97q−20 + 140q−22−132q−24 + 74q−26 + 17q−28−112q−30 + 178q−32−181q−34 + 132q−36−36q−38−62q−40 + 129q−42−147q−44 + 107q−46−35q−48−39q−50 + 81q−52−76q−54 + 28q−56 + 37q−58−86q−60 + 94q−62−64q−64 + q−66 + 61q−68−107q−70 + 119q−72−89q−74 + 41q−76 + 16q−78−61q−80 + 80q−82−76q−84 + 57q−86−25q−88−3q−90 + 23q−92−32q−94 + 30q−96−21q−98 + 12q−100−2q−102−4q−104 + 5q−106−6q−108 + 4q−110−2q−112 + q−114 |
Further Quantum Invariants
Further quantum knot invariants for 10_70.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q7−q5 + 3q3−3q + 2q−1−q−3 + 2q−7−3q−9 + 3q−11−2q−13 + q−15 |
| 2 | q22−q20−q18 + 5q16−3q14−8q12 + 13q10 + q8−19q6 + 15q4 + 11q2−23 + 7q−2 + 16q−4−15q−6−4q−8 + 12q−10 + q−12−12q−14 + q−16 + 18q−18−14q−20−11q−22 + 25q−24−8q−26−15q−28 + 16q−30−2q−32−8q−34 + 6q−36−2q−40 + q−42 |
| 3 | q45−q43−q41 + q39 + 4q37−3q35−9q33 + 2q31 + 19q29 + 3q27−30q25−18q23 + 42q21 + 40q19−41q17−69q15 + 28q13 + 97q11−6q9−110q7−28q5 + 113q3 + 60q−102q−1−84q−3 + 82q−5 + 98q−7−54q−9−103q−11 + 28q−13 + 100q−15−86q−19−31q−21 + 67q−23 + 61q−25−41q−27−89q−29 + 8q−31 + 108q−33 + 27q−35−113q−37−61q−39 + 106q−41 + 82q−43−84q−45−87q−47 + 55q−49 + 81q−51−32q−53−63q−55 + 16q−57 + 41q−59−6q−61−25q−63 + 3q−65 + 15q−67−3q−69−7q−71 + q−73 + 3q−75−2q−79 + q−81 |
| 4 | q76−q74−q72 + q70 + 4q66−5q64−7q62 + 4q60 + 6q58 + 21q56−11q54−36q52−15q50 + 14q48 + 86q46 + 26q44−76q42−110q40−60q38 + 172q36 + 182q34 + 3q32−223q30−308q28 + 93q26 + 359q24 + 306q22−122q20−577q18−250q16 + 281q14 + 626q12 + 267q10−557q8−618q6−95q4 + 668q2 + 660−241q−2−716q−4−472q−6 + 434q−8 + 789q−10 + 107q−12−569q−14−632q−16 + 156q−18 + 686q−20 + 315q−22−348q−24−609q−26−79q−28 + 480q−30 + 452q−32−90q−34−511q−36−340q−38 + 182q−40 + 565q−42 + 267q−44−296q−46−611q−48−251q−50 + 536q−52 + 630q−54 + 92q−56−682q−58−678q−60 + 251q−62 + 738q−64 + 489q−66−434q−68−794q−70−100q−72 + 485q−74 + 591q−76−79q−78−545q−80−233q−82 + 144q−84 + 391q−86 + 80q−88−229q−90−138q−92−15q−94 + 157q−96 + 57q−98−68q−100−34q−102−24q−104 + 48q−106 + 14q−108−23q−110−8q−114 + 14q−116 + 2q−118−8q−120 + 2q−122−2q−124 + 3q−126−2q−130 + q−132 |
| 5 | q115−q113−q111 + q109 + 2q103−3q101−6q99 + 4q97 + 9q95 + 6q93 + 3q91−16q89−32q87−12q85 + 33q83 + 62q81 + 51q79−23q77−122q75−139q73−26q71 + 167q69 + 283q67 + 174q65−149q63−450q61−449q59−31q57 + 571q55 + 826q53 + 417q51−472q49−1195q47−1057q45 + 59q43 + 1388q41 + 1786q39 + 737q37−1158q35−2424q33−1840q31 + 430q29 + 2697q27 + 2975q25 + 785q23−2366q21−3903q19−2282q17 + 1468q15 + 4314q13 + 3714q11−81q9−4092q7−4841q5−1459q3 + 3323q + 5406q−1 + 2871q−3−2184q−5−5405q−7−3922q−9 + 968q−11 + 4944q−13 + 4501q−15 + 95q−17−4211q−19−4618q−21−908q−23 + 3416q−25 + 4430q−27 + 1417q−29−2678q−31−4082q−33−1718q−35 + 2030q−37 + 3713q−39 + 1961q−41−1447q−43−3398q−45−2251q−47 + 820q−49 + 3094q−51 + 2688q−53−13q−55−2745q−57−3233q−59−1017q−61 + 2183q−63 + 3765q−65 + 2282q−67−1304q−69−4123q−71−3622q−73 + 86q−75 + 4064q−77 + 4820q−79 + 1406q−81−3501q−83−5627q−85−2893q−87 + 2444q−89 + 5778q−91 + 4138q−93−1068q−95−5269q−97−4847q−99−306q−101 + 4206q−103 + 4863q−105 + 1425q−107−2857q−109−4306q−111−2051q−113 + 1572q−115 + 3346q−117 + 2142q−119−550q−121−2285q−123−1857q−125−66q−127 + 1372q−129 + 1367q−131 + 306q−133−693q−135−874q−137−330q−139 + 297q−141 + 498q−143 + 237q−145−113q−147−238q−149−135q−151 + 29q−153 + 106q−155 + 70q−157−16q−159−46q−161−20q−163 + 8q−165 + 15q−167 + 6q−169−2q−171−11q−173−2q−175 + 9q−177 + q−179−3q−181 + q−183−q−185−2q−187 + 3q−189−2q−193 + q−195 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q10 + q8 + 2q4−2q2−1 + q−2−2q−4 + 3q−6−q−8 + q−10−2q−14 + 2q−16−q−18 + q−22 |
| 2,0 | q28 + q26−q22 + 2q20 + 3q18−3q16−7q14 + 2q12 + 6q10−3q8−6q6 + 7q4 + 11q2−7−7q−2 + 8q−4 + q−6−8q−8 + 6q−12−3q−14−2q−16 + 8q−18−q−20−9q−22 + 5q−24 + 9q−26−9q−28−5q−30 + 10q−32 + 4q−34−8q−36−4q−38 + 7q−40 + q−42−5q−44 + 2q−48−q−52 + q−56 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q20−q18 + 2q16 + 3q14−4q12 + 5q10 + 5q8−13q6 + 8q4 + 5q2−19 + 10q−2 + 8q−4−16q−6 + 6q−8 + 11q−10−6q−12−2q−14 + 4q−16 + 5q−18−9q−20−6q−22 + 16q−24−10q−26−10q−28 + 20q−30−6q−32−10q−34 + 14q−36−2q−38−7q−40 + 5q−42−2q−46 + q−48 |
| 1,0,0 | q13 + q11 + 2q9 + 2q5−3q3−3q−1 + q−3−q−5 + 2q−7 + 2q−9 + q−13−2q−15 + q−17−3q−19 + 2q−21−q−23 + q−25 + q−29 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | q20−q18 + 4q16−5q14 + 10q12−13q10 + 17q8−19q6 + 20q4−19q2 + 13−8q−2−2q−4 + 12q−6−22q−8 + 31q−10−36q−12 + 40q−14−38q−16 + 33q−18−25q−20 + 16q−22−6q−24−4q−26 + 12q−28−18q−30 + 20q−32−20q−34 + 18q−36−14q−38 + 11q−40−7q−42 + 4q−44−2q−46 + q−48 |
| 1,0 | q34−q30−q28 + 3q26 + 4q24−q22−7q20−2q18 + 10q16 + 10q14−8q12−17q10−q8 + 20q6 + 11q4−17q2−19 + 6q−2 + 22q−4 + 4q−6−18q−8−10q−10 + 12q−12 + 12q−14−7q−16−11q−18 + 5q−20 + 13q−22−2q−24−14q−26−q−28 + 15q−30 + 5q−32−15q−34−11q−36 + 13q−38 + 16q−40−8q−42−21q−44−q−46 + 21q−48 + 11q−50−13q−52−17q−54 + 3q−56 + 16q−58 + 6q−60−8q−62−9q−64 + q−66 + 6q−68 + 2q−70−2q−72−2q−74 + q−78 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q46−q44 + 4q42−5q40 + 6q38−5q36 + 12q32−23q30 + 36q28−37q26 + 25q24 + 5q22−42q20 + 80q18−97q16 + 85q14−40q12−32q10 + 96q8−132q6 + 124q4−70q2−6 + 70q−2−108q−4 + 90q−6−38q−8−31q−10 + 81q−12−86q−14 + 46q−16 + 27q−18−97q−20 + 140q−22−132q−24 + 74q−26 + 17q−28−112q−30 + 178q−32−181q−34 + 132q−36−36q−38−62q−40 + 129q−42−147q−44 + 107q−46−35q−48−39q−50 + 81q−52−76q−54 + 28q−56 + 37q−58−86q−60 + 94q−62−64q−64 + q−66 + 61q−68−107q−70 + 119q−72−89q−74 + 41q−76 + 16q−78−61q−80 + 80q−82−76q−84 + 57q−86−25q−88−3q−90 + 23q−92−32q−94 + 30q−96−21q−98 + 12q−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 70"];
|
In[4]:=
| Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| t3−7t2 + 16t−19 + 16t−1−7t−2 + t−3 |
In[5]:=
| Conway[K][z]
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Out[5]=
| z6−z4−3z2 + 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]=
| { 67, 2 } |
In[8]:=
| Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
| q7−3q6 + 6q5−9q4 + 11q3−11q2 + 10q−8 + 5q−1−2q−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 + 4z2a−2−4z2a−4 + z2a−6−5z2 + 2a2 + 3a−2−2a−4 + a−6−3 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| z9a−1 + z9a−3 + 5z8a−2 + 3z8a−4 + 2z8 + 2az7 + 3z7a−1 + 6z7a−3 + 5z7a−5 + a2z6−5z6a−2 + 3z6a−4 + 5z6a−6−2z6−6az5−10z5a−1−11z5a−3−4z5a−5 + 3z5a−7−4a2z4−8z4a−2−12z4a−4−6z4a−6 + z4a−8−7z4 + 5az3 + 4z3a−1 + 2z3a−3−3z3a−7 + 5a2z2 + 9z2a−2 + 9z2a−4 + 4z2a−6−z2a−8 + 10z2−az + za−3 + za−5 + za−7−2a2−3a−2−2a−4−a−6−3 |
[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 70"];
|
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 + 16t−19 + 16t−1−7t−2 + t−3, q7−3q6 + 6q5−9q4 + 11q3−11q2 + 10q−8 + 5q−1−2q−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]=
| {} |
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] 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 70. 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 + 7q17−17q16 + 8q15 + 25q14−48q13 + 15q12 + 58q11−84q10 + 12q9 + 90q8−101q7−q6 + 103q5−90q4−17q3 + 92q2−59q−26 + 62q−1−25q−2−22q−3 + 28q−4−5q−5−10q−6 + 7q−7−2q−9 + q−10 |
| 3 | q39−3q38 + 2q37 + 3q36−q35−11q34 + 6q33 + 21q32−13q31−39q30 + 25q29 + 68q28−38q27−118q26 + 56q25 + 181q24−64q23−260q22 + 59q21 + 347q20−40q19−427q18 + 7q17 + 487q16 + 41q15−527q14−90q13 + 535q12 + 143q11−521q10−188q9 + 480q8 + 229q7−421q6−260q5 + 349q4 + 278q3−269q2−276q + 183 + 260q−1−107q−2−223q−3 + 42q−4 + 178q−5−3q−6−120q−7−27q−8 + 81q−9 + 25q−10−39q−11−25q−12 + 21q−13 + 13q−14−6q−15−9q−16 + 4q−17 + 2q−18−2q−20 + q−21 |
| 4 | q64−3q63 + 2q62 + 3q61−5q60 + 5q59−13q58 + 12q57 + 15q56−27q55 + 13q54−36q53 + 49q52 + 49q51−99q50 + 3q49−70q48 + 174q47 + 149q46−271q45−120q44−161q43 + 483q42 + 460q41−518q40−497q39−473q38 + 949q37 + 1130q36−624q35−1082q34−1167q33 + 1309q32 + 2053q31−375q30−1569q29−2096q28 + 1305q27 + 2827q26 + 163q25−1663q24−2883q23 + 945q22 + 3142q21 + 726q20−1365q19−3266q18 + 423q17 + 2971q16 + 1147q15−823q14−3238q13−136q12 + 2441q11 + 1408q10−160q9−2867q8−666q7 + 1653q6 + 1471q5 + 516q4−2185q3−1021q2 + 747q + 1227 + 991q−1−1284q−2−1013q−3−16q−4 + 704q−5 + 1052q−6−460q−7−654q−8−361q−9 + 173q−10 + 725q−11−5q−12−226q−13−308q−14−93q−15 + 324q−16 + 80q−17−129q−19−103q−20 + 92q−21 + 30q−22 + 34q−23−27q−24−43q−25 + 20q−26 + q−27 + 13q−28−2q−29−11q−30 + 5q−31−q−32 + 2q−33−2q−35 + q−36 |
| 5 | q95−3q94 + 2q93 + 3q92−5q91 + q90 + 3q89−7q88 + 6q87 + 11q86−16q85−8q84 + 12q83 + q82 + 15q81 + 4q80−44q79−34q78 + 42q77 + 87q76 + 51q75−73q74−208q73−137q72 + 167q71 + 437q70 + 312q69−274q68−835q67−681q66 + 348q65 + 1436q64 + 1373q63−269q62−2273q61−2472q60−80q59 + 3171q58 + 4065q57 + 935q56−4047q55−6095q54−2335q53 + 4620q52 + 8347q51 + 4373q50−4704q49−10607q48−6876q47 + 4198q46 + 12548q45 + 9579q44−3064q43−13941q42−12213q41 + 1464q40 + 14674q39 + 14486q38 + 350q37−14697q36−16191q35−2244q34 + 14173q33 + 17305q32 + 3936q31−13214q30−17773q29−5444q28 + 11957q27 + 17793q26 + 6668q25−10513q24−17367q23−7718q22 + 8886q21 + 16646q20 + 8619q19−7105q18−15615q17−9401q16 + 5138q15 + 14282q14 + 10023q13−3010q12−12602q11−10415q10 + 814q9 + 10572q8 + 10430q7 + 1296q6−8196q5−9972q4−3162q3 + 5682q2 + 8947q + 4517−3141q−1−7437q−2−5245q−3 + 900q−4 + 5565q−5 + 5266q−6 + 870q−7−3642q−8−4645q−9−1946q−10 + 1815q−11 + 3645q−12 + 2407q−13−491q−14−2455q−15−2224q−16−452q−17 + 1375q−18 + 1823q−19 + 775q−20−560q−21−1175q−22−850q−23 + 46q−24 + 707q−25 + 637q−26 + 163q−27−286q−28−441q−29−209q−30 + 105q−31 + 219q−32 + 162q−33 + 15q−34−118q−35−100q−36−11q−37 + 26q−38 + 49q−39 + 32q−40−19q−41−26q−42−3q−44 + 4q−45 + 12q−46−3q−47−7q−48 + 3q−49−q−51 + 2q−52−2q−54 + q−55 |
| 6 | q132−3q131 + 2q130 + 3q129−5q128 + q127−q126 + 9q125−13q124 + 2q123 + 22q122−27q121−q120 + 4q119 + 34q118−36q117−15q116 + 62q115−76q114 + q113 + 48q112 + 120q111−105q110−118q109 + 68q108−209q107 + 82q106 + 303q105 + 468q104−208q103−563q102−329q101−769q100 + 296q99 + 1335q98 + 1900q97 + 163q96−1641q95−2263q94−3195q93−80q92 + 3845q91 + 6496q90 + 3249q89−2433q88−7081q87−10749q86−4297q85 + 6688q84 + 16430q83 + 13649q82 + 1459q81−13393q80−26300q79−18239q78 + 4228q77 + 29736q76 + 34569q75 + 17057q74−14246q73−46801q72−44892q71−11370q70 + 37819q69 + 61374q68 + 46633q67−1246q66−61813q65−77627q64−41330q63 + 31612q62 + 81939q61 + 81732q60 + 25819q59−61850q58−103039q57−75846q56 + 11423q55 + 86852q54 + 108599q53 + 56676q52−47652q51−112329q50−101819q49−13005q48 + 77413q47 + 119771q46 + 79786q45−28125q44−107350q43−113575q42−32309q41 + 61603q40 + 117779q39 + 91486q38−10585q37−95095q36−114274q35−44687q34 + 44956q33 + 108708q32 + 95399q31 + 4470q30−79576q29−109084q28−53794q27 + 27115q26 + 95237q25 + 95588q24 + 20213q23−59806q22−99283q21−62145q20 + 5585q19 + 75646q18 + 91588q17 + 37316q16−33836q15−82040q14−67029q13−18577q12 + 48061q11 + 78980q10 + 50761q9−4104q8−55164q7−62105q6−38341q5 + 15871q4 + 55016q3 + 52520q2 + 20731q−22807−44078q−1−44550q−2−11026q−3 + 24632q−4 + 39273q−5 + 30852q−6 + 4104q−7−18706q−8−34494q−9−22650q−10−415q−11 + 17893q−12 + 24460q−13 + 15849q−14 + 1816q−15−16305q−16−18376q−17−11053q−18 + 783q−19 + 10573q−20 + 13052q−21 + 9531q−22−2150q−23−7705q−24−9079q−25−5370q−26 + 390q−27 + 5184q−28 + 7230q−29 + 2754q−30−408q−31−3408q−32−3874q−33−2504q−34 + 243q−35 + 2775q−36 + 1961q−37 + 1388q−38−189q−39−1166q−40−1587q−41−787q−42 + 472q−43 + 471q−44 + 773q−45 + 385q−46−q−47−493q−48−402q−49−5q−50−54q−51 + 185q−52 + 169q−53 + 125q−54−92q−55−103q−56 + 7q−57−62q−58 + 14q−59 + 30q−60 + 52q−61−18q−62−22q−63 + 17q−64−17q−65−2q−66 + 14q−68−4q−69−8q−70 + 7q−71−2q−72−q−74 + 2q−75−2q−77 + q−78 |
| 7 | q175−3q174 + 2q173 + 3q172−5q171 + q170−q169 + 5q168 + 3q167−17q166 + 13q165 + 11q164−20q163 + q162−4q161 + 23q160 + 12q159−63q158 + 29q157 + 34q156−34q155 + 23q154−18q153 + 55q152 + 12q151−198q150 + 3q149 + 71q148 + 47q147 + 230q146 + 50q145 + 66q144−145q143−724q142−353q141 + 13q140 + 520q139 + 1332q138 + 905q137 + 355q136−917q135−2821q134−2515q133−1150q132 + 1663q131 + 5288q130 + 5510q129 + 3362q128−1969q127−9162q126−11357q125−8441q124 + 1161q123 + 14604q122 + 21112q121 + 18248q120 + 2916q119−20569q118−35846q117−35729q116−13536q115 + 25131q114 + 55814q113 + 63421q112 + 34626q111−24306q110−79032q109−102766q108−71016q107 + 12239q106 + 101698q105 + 153512q104 + 125905q103 + 16684q102−117126q101−211154q100−199960q99−68480q98 + 117353q97 + 269308q96 + 290136q95 + 144840q94−95578q93−318013q92−388563q91−243972q90 + 46842q89 + 348054q88 + 485310q87 + 358866q86 + 28223q85−352749q84−568558q83−478520q82−124621q81 + 328979q80 + 629170q79 + 591488q78 + 232801q77−279871q76−661976q75−686486q74−341333q73 + 212051q72 + 666409q71 + 756673q70 + 440078q69−134955q68−647158q67−799961q66−520882q65 + 58293q64 + 610871q63 + 817822q62 + 580697q61 + 11462q60−565695q59−816163q58−619888q57−69492q56 + 517939q55 + 800398q54 + 642024q53 + 116278q52−471442q51−777066q50−652394q49−153511q48 + 427655q47 + 749531q46 + 655627q45 + 185625q44−384785q43−719796q42−655999q41−216663q40 + 340338q39 + 687199q38 + 654998q37 + 250045q36−290443q35−649412q34−652647q33−287586q32 + 232233q31 + 603323q30 + 646536q29 + 328734q28−164024q27−545504q26−632755q25−370794q24 + 86148q23 + 473466q22 + 606939q21 + 408848q20−1685q19−386702q18−564654q17−436469q16−83924q15 + 287144q14 + 503101q13 + 447272q12 + 163191q11−180012q10−422607q9−435763q8−227138q7 + 73008q6 + 326292q5 + 399434q4 + 268705q3 + 24117q2−221975q−339762−282160q−1−101787q−2 + 118926q−3 + 262600q−4 + 267060q−5 + 152844q−6−28173q−7−177405q−8−227350q−9−174130q−10−41158q−11 + 95277q−12 + 171190q−13 + 167388q−14 + 84278q−15−26119q−16−109769q−17−139868q−18−100408q−19−22429q−20 + 52993q−21 + 100264q−22 + 94696q−23 + 49423q−24−9197q−25−59862q−26−74724q−27−55918q−28−18180q−29 + 25011q−30 + 49184q−31 + 49310q−32 + 30175q−33−1650q−34−25698q−35−35107q−36−30072q−37−11113q−38 + 7919q−39 + 20617q−40 + 23757q−41 + 14479q−42 + 2152q−43−8699q−44−15163q−45−12732q−46−6330q−47 + 1416q−48 + 7932q−49 + 8608q−50 + 6383q−51 + 2116q−52−2954q−53−4822q−54−4734q−55−2785q−56 + 374q−57 + 1933q−58 + 2786q−59 + 2423q−60 + 587q−61−550q−62−1354q−63−1434q−64−631q−65−213q−66 + 446q−67 + 864q−68 + 490q−69 + 218q−70−137q−71−324q−72−175q−73−247q−74−81q−75 + 171q−76 + 125q−77 + 112q−78 + 4q−79−47q−80 + 22q−81−62q−82−62q−83 + 19q−84 + 18q−85 + 32q−86−4q−87−19q−88 + 25q−89−4q−90−16q−91 + 10q−94−2q−95−9q−96 + 6q−97 + 2q−98−2q−99−q−101 + 2q−102−2q−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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