9 21
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 9 21's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9_21's page at Knotilus! Visit 9 21's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X1425 X9,12,10,13 X3,11,4,10 X11,3,12,2 X13,1,14,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 |
| Gauss code | -1, 4, -3, 1, -6, 7, -8, 9, -2, 3, -4, 2, -5, 6, -9, 8, -7, 5 |
| Dowker-Thistlethwaite code | 4 10 14 16 12 2 18 8 6 |
| Conway Notation | [31122] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 | 
|  [{11, 6}, {7, 5}, {6, 10}, {1, 7}, {8, 11}, {10, 4}, {5, 2}, {3, 1}, {4, 9}, {2, 8}, {9, 3}] |
[edit Notes on presentations of 9 21]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["9 21"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X1425 X9,12,10,13 X3,11,4,10 X11,3,12,2 X13,1,14,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 |
In[5]:=
| GaussCode[K]
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Out[5]=
| -1, 4, -3, 1, -6, 7, -8, 9, -2, 3, -4, 2, -5, 6, -9, 8, -7, 5 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 10 14 16 12 2 18 8 6 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [31122] |
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,{1,1,2,−1,2,−3,2,4,−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[{11, 6}, {7, 5}, {6, 10}, {1, 7}, {8, 11}, {10, 4}, {5, 2}, {3, 1}, {4, 9}, {2, 8}, {9, 3}] |
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 | −2t2 + 11t−17 + 11t−1−2t−2 |
| Conway polynomial | −2z4 + 3z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 43, 2 } |
| Jones polynomial | −q8 + 2q7−4q6 + 6q5−7q4 + 8q3−6q2 + 5q−3 + q−1 |
| HOMFLY-PT polynomial (db, data sources) | −z4a−2−z4a−4 + 2z2a−6 + z2 + a−2 + a−6−a−8 |
| Kauffman polynomial (db, data sources) | z8a−4 + z8a−6 + 3z7a−3 + 5z7a−5 + 2z7a−7 + 4z6a−2 + 4z6a−4 + 2z6a−6 + 2z6a−8 + 3z5a−1−3z5a−3−10z5a−5−3z5a−7 + z5a−9−6z4a−2−9z4a−4−7z4a−6−5z4a−8 + z4−4z3a−1 + 2z3a−3 + 9z3a−5−3z3a−9 + 3z2a−2 + 6z2a−4 + 5z2a−6 + 3z2a−8−z2−za−3−3za−5 + 2za−9−a−2−a−6−a−8 |
| The A2 invariant | q4−q2−1 + 2q−2−q−4 + 2q−6 + q−8 + q−12−q−14 + 2q−16−q−20 + q−22−q−24−q−26 |
| The G2 invariant | q18−2q16 + 4q14−6q12 + 4q10−q8−4q6 + 13q4−17q2 + 22−19q−2 + 5q−4 + 10q−6−27q−8 + 38q−10−39q−12 + 28q−14−7q−16−17q−18 + 36q−20−40q−22 + 30q−24−9q−26−13q−28 + 24q−30−21q−32 + 8q−34 + 18q−36−33q−38 + 40q−40−24q−42−4q−44 + 36q−46−58q−48 + 63q−50−46q−52 + 17q−54 + 18q−56−45q−58 + 57q−60−50q−62 + 27q−64−25q−68 + 32q−70−23q−72 + 7q−74 + 16q−76−28q−78 + 26q−80−10q−82−14q−84 + 36q−86−44q−88 + 36q−90−17q−92−8q−94 + 27q−96−37q−98 + 35q−100−23q−102 + 6q−104 + 6q−106−16q−108 + 16q−110−14q−112 + 9q−114−3q−116−2q−118 + 3q−120−4q−122 + 3q−124−q−126 + q−128 |
Further Quantum Invariants
Further quantum knot invariants for 9_21.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q3−2q + 2q−1−q−3 + 2q−5 + q−7−q−9 + 2q−11−2q−13 + q−15−q−17 |
| 2 | q10−2q8−q6 + 6q4−4q2−5 + 11q−2−3q−4−9q−6 + 11q−8 + q−10−8q−12 + 5q−14 + 4q−16−2q−18−5q−20 + 6q−22 + 5q−24−11q−26 + 3q−28 + 8q−30−11q−32−q−34 + 8q−36−5q−38−2q−40 + 4q−42−q−44−q−46 + q−48 |
| 3 | q21−2q19−q17 + 3q15 + 3q13−4q11−8q9 + 8q7 + 13q5−9q3−21q + 7q−1 + 32q−3−3q−5−40q−7−5q−9 + 46q−11 + 14q−13−41q−15−22q−17 + 38q−19 + 26q−21−25q−23−28q−25 + 13q−27 + 25q−29 + 2q−31−21q−33−16q−35 + 20q−37 + 26q−39−12q−41−38q−43 + 6q−45 + 42q−47 + q−49−46q−51−10q−53 + 41q−55 + 19q−57−36q−59−24q−61 + 24q−63 + 27q−65−13q−67−23q−69 + 5q−71 + 17q−73 + q−75−11q−77−2q−79 + 6q−81 + 2q−83−3q−85−q−87 + q−89 + q−91−q−93 |
| 4 | q36−2q34−q32 + 3q30 + 3q26−7q24−3q22 + 9q20 + q18 + 9q16−22q14−16q12 + 22q10 + 21q8 + 29q6−50q4−59q2 + 16 + 62q−2 + 97q−4−54q−6−135q−8−51q−10 + 79q−12 + 191q−14 + 6q−16−168q−18−144q−20 + 28q−22 + 231q−24 + 92q−26−118q−28−179q−30−51q−32 + 173q−34 + 128q−36−27q−38−136q−40−97q−42 + 68q−44 + 109q−46 + 52q−48−59q−50−104q−52−38q−54 + 77q−56 + 114q−58 + 5q−60−107q−62−126q−64 + 47q−66 + 162q−68 + 69q−70−94q−72−198q−74−2q−76 + 178q−78 + 135q−80−42q−82−224q−84−75q−86 + 123q−88 + 168q−90 + 50q−92−170q−94−123q−96 + 20q−98 + 125q−100 + 110q−102−65q−104−96q−106−50q−108 + 42q−110 + 91q−112 + 4q−114−33q−116−47q−118−8q−120 + 39q−122 + 13q−124 + q−126−19q−128−11q−130 + 11q−132 + 3q−134 + 4q−136−4q−138−4q−140 + 3q−142 + q−146−q−148−q−150 + q−152 |
| 5 | q55−2q53−q51 + 3q49−2q41−2q39 + 5q37 + 4q35−6q33−8q31−5q29 + 6q27 + 18q25 + 24q23−3q21−46q19−51q17−10q15 + 62q13 + 109q11 + 65q9−75q7−195q5−154q3 + 44q + 271q−1 + 307q−3 + 54q−5−326q−7−489q−9−214q−11 + 313q−13 + 652q−15 + 448q−17−214q−19−771q−21−680q−23 + 38q−25 + 782q−27 + 884q−29 + 188q−31−703q−33−984q−35−407q−37 + 529q−39 + 991q−41 + 568q−43−320q−45−875q−47−655q−49 + 101q−51 + 710q−53 + 657q−55 + 70q−57−492q−59−598q−61−214q−63 + 299q−65 + 509q−67 + 303q−69−122q−71−417q−73−373q−75−36q−77 + 353q−79 + 446q−81 + 147q−83−302q−85−520q−87−281q−89 + 266q−91 + 622q−93 + 398q−95−228q−97−701q−99−552q−101 + 156q−103 + 774q−105 + 703q−107−39q−109−782q−111−844q−113−126q−115 + 722q−117 + 932q−119 + 326q−121−568q−123−957q−125−506q−127 + 348q−129 + 865q−131 + 645q−133−88q−135−699q−137−689q−139−133q−141 + 458q−143 + 632q−145 + 303q−147−218q−149−501q−151−364q−153 + 17q−155 + 324q−157 + 340q−159 + 111q−161−160q−163−263q−165−154q−167 + 40q−169 + 161q−171 + 142q−173 + 28q−175−80q−177−102q−179−46q−181 + 26q−183 + 60q−185 + 38q−187−q−189−27q−191−27q−193−5q−195 + 13q−197 + 12q−199 + 3q−201−q−203−6q−205−4q−207 + 3q−209 + 2q−211−q−213−q−219 + q−221 + q−223−q−225 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q4−q2−1 + 2q−2−q−4 + 2q−6 + q−8 + q−12−q−14 + 2q−16−q−20 + q−22−q−24−q−26 |
| 1,1 | q12−4q10 + 10q8−20q6 + 34q4−52q2 + 78−104q−2 + 124q−4−142q−6 + 152q−8−140q−10 + 113q−12−60q−14 + 2q−16 + 74q−18−150q−20 + 220q−22−268q−24 + 298q−26−297q−28 + 272q−30−228q−32 + 162q−34−89q−36 + 14q−38 + 50q−40−100q−42 + 136q−44−152q−46 + 144q−48−130q−50 + 106q−52−82q−54 + 56q−56−36q−58 + 23q−60−12q−62 + 6q−64−2q−66 + q−68 |
| 2,0 | q12−q10−2q8 + q6 + 4q4 + q2−7−q−2 + 8q−4−7q−8 + 2q−10 + 8q−12−4q−16 + 2q−18 + 4q−20−3q−22 + q−24 + 2q−26−2q−28 + 2q−30 + 7q−32−q−34−6q−36 + q−38 + 5q−40−4q−42−9q−44 + q−46 + 5q−48−q−50−4q−52 + 3q−56−2q−60 + q−64 + q−66 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q8−2q6 + 4q2−5 + q−2 + 8q−4−8q−6−q−8 + 9q−10−6q−12−2q−14 + 8q−16 + 2q−22 + 5q−24−q−26−6q−28 + 6q−30 + q−32−10q−34 + 6q−36 + 2q−38−9q−40 + 3q−42 + q−44−4q−46 + 2q−48 + q−50−q−52 + q−54 |
| 1,0,0 | q5−q3−q−1 + 2q−3−q−5 + 2q−7 + q−9 + q−11 + q−17−q−19 + 2q−21 + q−25−q−27 + q−29−q−31−q−33−q−35 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | q8−2q6 + 4q4−6q2 + 7−9q−2 + 10q−4−8q−6 + 7q−8−3q−10 + 6q−14−10q−16 + 14q−18−16q−20 + 18q−22−17q−24 + 15q−26−10q−28 + 6q−30−q−32−2q−34 + 6q−36−8q−38 + 9q−40−9q−42 + 7q−44−6q−46 + 4q−48−3q−50 + q−52−q−54 |
| 1,0 | q14−2q10−2q8 + 2q6 + 5q4−6−4q−2 + 6q−4 + 9q−6−2q−8−10q−10−4q−12 + 8q−14 + 7q−16−4q−18−8q−20 + 2q−22 + 8q−24 + 2q−26−6q−28−q−30 + 7q−32 + 5q−34−4q−36−4q−38 + 4q−40 + 6q−42−3q−44−7q−46 + q−48 + 8q−50 + q−52−9q−54−7q−56 + 6q−58 + 9q−60−2q−62−10q−64−4q−66 + 6q−68 + 5q−70−2q−72−5q−74−q−76 + 3q−78 + 2q−80−q−82−q−84 + q−88 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q18−2q16 + 4q14−6q12 + 4q10−q8−4q6 + 13q4−17q2 + 22−19q−2 + 5q−4 + 10q−6−27q−8 + 38q−10−39q−12 + 28q−14−7q−16−17q−18 + 36q−20−40q−22 + 30q−24−9q−26−13q−28 + 24q−30−21q−32 + 8q−34 + 18q−36−33q−38 + 40q−40−24q−42−4q−44 + 36q−46−58q−48 + 63q−50−46q−52 + 17q−54 + 18q−56−45q−58 + 57q−60−50q−62 + 27q−64−25q−68 + 32q−70−23q−72 + 7q−74 + 16q−76−28q−78 + 26q−80−10q−82−14q−84 + 36q−86−44q−88 + 36q−90−17q−92−8q−94 + 27q−96−37q−98 + 35q−100−23q−102 + 6q−104 + 6q−106−16q−108 + 16q−110−14q−112 + 9q−114−3q−116−2q−118 + 3q−120−4q−122 + 3q−124−q−126 + q−128 |
.
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["9 21"];
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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]=
| −2t2 + 11t−17 + 11t−1−2t−2 |
In[5]:=
| Conway[K][z]
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Out[5]=
| −2z4 + 3z2 + 1 |
In[6]:=
| 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.
|
Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
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Out[7]=
| { 43, 2 } |
In[8]:=
| Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
| −q8 + 2q7−4q6 + 6q5−7q4 + 8q3−6q2 + 5q−3 + q−1 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| −z4a−2−z4a−4 + 2z2a−6 + z2 + a−2 + a−6−a−8 |
In[10]:=
| Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
| z8a−4 + z8a−6 + 3z7a−3 + 5z7a−5 + 2z7a−7 + 4z6a−2 + 4z6a−4 + 2z6a−6 + 2z6a−8 + 3z5a−1−3z5a−3−10z5a−5−3z5a−7 + z5a−9−6z4a−2−9z4a−4−7z4a−6−5z4a−8 + z4−4z3a−1 + 2z3a−3 + 9z3a−5−3z3a−9 + 3z2a−2 + 6z2a−4 + 5z2a−6 + 3z2a−8−z2−za−3−3za−5 + 2za−9−a−2−a−6−a−8 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, 
):
{K11n129,}
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["9 21"];
|
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]=
| { −2t2 + 11t−17 + 11t−1−2t−2, −q8 + 2q7−4q6 + 6q5−7q4 + 8q3−6q2 + 5q−3 + q−1 } |
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]=
| {K11n129,} |
[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 9 21. 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 | q23−2q22 + 6q20−8q19−3q18 + 19q17−17q16−13q15 + 38q14−22q13−27q12 + 54q11−21q10−38q9 + 57q8−15q7−37q6 + 44q5−6q4−27q3 + 24q2−13 + 8q−1 + q−2−3q−3 + q−4 |
| 3 | −q45 + 2q44−2q42−3q41 + 7q40 + 4q39−10q38−12q37 + 19q36 + 20q35−22q34−40q33 + 29q32 + 60q31−25q30−88q29 + 17q28 + 115q27−3q26−139q25−19q24 + 162q23 + 38q22−175q21−63q20 + 188q19 + 76q18−181q17−99q16 + 183q15 + 99q14−158q13−111q12 + 142q11 + 102q10−107q9−99q8 + 82q7 + 83q6−52q5−67q4 + 31q3 + 48q2−15q−32 + 6q−1 + 20q−2−3q−3−10q−4 + q−5 + 4q−6 + q−7−3q−8 + q−9 |
| 4 | q74−2q73 + 2q71−q70 + 4q69−9q68 + 10q66−2q65 + 12q64−31q63−8q62 + 30q61 + 10q60 + 38q59−78q58−47q57 + 44q56 + 47q55 + 125q54−127q53−139q52−2q51 + 78q50 + 300q49−112q48−244q47−145q46 + 31q45 + 520q44 + 6q43−289q42−343q41−118q40 + 702q39 + 183q38−246q37−523q36−314q35 + 806q34 + 346q33−153q32−638q31−487q30 + 825q29 + 458q28−44q27−675q26−602q25 + 759q24 + 503q23 + 67q22−618q21−643q20 + 594q19 + 464q18 + 176q17−463q16−598q15 + 370q14 + 336q13 + 237q12−253q11−459q10 + 167q9 + 164q8 + 213q7−79q6−274q5 + 55q4 + 34q3 + 129q2 + 2q−123 + 20q−1−12q−2 + 54q−3 + 11q−4−44q−5 + 12q−6−11q−7 + 16q−8 + 5q−9−13q−10 + 4q−11−3q−12 + 4q−13 + q−14−3q−15 + q−16 |
| 5 | −q110 + 2q109−2q107 + q106−2q104 + 5q103 + q102−9q101−q100 + 5q99 + 2q98 + 14q97 + 2q96−27q95−23q94 + 5q93 + 28q92 + 53q91 + 24q90−61q89−95q88−51q87 + 50q86 + 161q85 + 138q84−42q83−216q82−245q81−59q80 + 264q79 + 409q78 + 187q77−232q76−552q75−440q74 + 127q73 + 692q72 + 708q71 + 97q70−726q69−1031q68−429q67 + 682q66 + 1319q65 + 830q64−506q63−1548q62−1283q61 + 231q60 + 1708q59 + 1724q58 + 100q57−1758q56−2131q55−487q54 + 1770q53 + 2467q52 + 842q51−1687q50−2749q49−1195q48 + 1621q47 + 2940q46 + 1468q45−1463q44−3105q43−1742q42 + 1382q41 + 3158q40 + 1917q39−1164q38−3198q37−2131q36 + 1045q35 + 3114q34 + 2212q33−739q32−2992q31−2341q30 + 532q29 + 2730q28 + 2318q27−177q26−2405q25−2288q24−77q23 + 1974q22 + 2098q21 + 378q20−1517q19−1865q18−539q17 + 1038q16 + 1521q15 + 659q14−626q13−1169q12−641q11 + 294q10 + 803q9 + 568q8−69q7−507q6−437q5−45q4 + 276q3 + 293q2 + 94q−127−184q−1−81q−2 + 49q−3 + 95q−4 + 53q−5−7q−6−44q−7−37q−8 + 2q−9 + 23q−10 + 12q−11−2q−12−q−13−10q−14−4q−15 + 11q−16 + q−17−5q−18 + q−19−3q−21 + 4q−22 + q−23−3q−24 + q−25 |
| 6 | q153−2q152 + 2q150−q149−2q147 + 6q146−6q145−2q144 + 11q143−3q142−4q141−13q140 + 15q139−12q138−2q137 + 40q136 + 5q135−13q134−55q133 + 11q132−40q131 + 123q129 + 70q128 + 10q127−140q126−54q125−175q124−67q123 + 257q122 + 283q121 + 212q120−147q119−148q118−548q117−432q116 + 213q115 + 571q114 + 754q113 + 268q112 + 108q111−1003q110−1279q109−499q108 + 387q107 + 1340q106 + 1291q105 + 1343q104−779q103−2139q102−2047q101−1012q100 + 990q99 + 2286q98 + 3647q97 + 947q96−1858q95−3616q94−3609q93−1140q92 + 2000q91 + 6025q90 + 4038q89 + 347q88−3910q87−6293q86−4749q85−209q84 + 7174q83 + 7295q82 + 4009q81−2419q80−7843q79−8568q78−3712q77 + 6702q76 + 9565q75 + 7832q74 + 172q73−7986q72−11495q71−7246q70 + 5260q69 + 10601q68 + 10808q67 + 2762q66−7292q65−13269q64−9958q63 + 3692q62 + 10823q61 + 12730q60 + 4755q59−6367q58−14165q57−11759q56 + 2300q55 + 10589q54 + 13842q53 + 6259q52−5291q51−14366q50−12922q49 + 804q48 + 9790q47 + 14251q46 + 7601q45−3686q44−13634q43−13488q42−1121q41 + 7974q40 + 13616q39 + 8730q38−1279q37−11490q36−13007q35−3237q34 + 4967q33 + 11417q32 + 9006q31 + 1493q30−7898q29−10923q28−4636q27 + 1467q26 + 7737q25 + 7748q24 + 3485q23−3817q22−7419q21−4482q20−1153q19 + 3722q18 + 5140q17 + 3793q16−754q15−3722q14−2957q13−2008q12 + 860q11 + 2376q10 + 2690q9 + 525q8−1187q7−1203q6−1489q5−297q4 + 600q3 + 1306q2 + 522q−136−164q−1−670q−2−356q−3−44q−4 + 448q−5 + 191q−6 + 44q−7 + 128q−8−191q−9−149q−10−105q−11 + 126q−12 + 19q−13 + 3q−14 + 97q−15−35q−16−35q−17−46q−18 + 42q−19−11q−20−13q−21 + 34q−22−7q−23−4q−24−14q−25 + 18q−26−4q−27−9q−28 + 9q−29−3q−30−3q−32 + 4q−33 + q−34−3q−35 + q−36 |
[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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