9 14
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 9 14's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9_14's page at Knotilus! Visit 9 14's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X13,18,14,1 X9,15,10,14 X7,17,8,16 X15,9,16,8 X17,7,18,6 |
| Gauss code | -1, 4, -3, 1, -2, 9, -7, 8, -6, 3, -4, 2, -5, 6, -8, 7, -9, 5 |
| Dowker-Thistlethwaite code | 4 10 12 16 14 2 18 8 6 |
| Conway Notation | [41112] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 | 
|  [{11, 3}, {2, 9}, {10, 4}, {3, 5}, {9, 11}, {4, 1}, {6, 2}, {5, 7}, {8, 6}, {7, 10}, {1, 8}] |
[edit Notes on presentations of 9 14]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["9 14"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X13,18,14,1 X9,15,10,14 X7,17,8,16 X15,9,16,8 X17,7,18,6 |
In[5]:=
| GaussCode[K]
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Out[5]=
| -1, 4, -3, 1, -2, 9, -7, 8, -6, 3, -4, 2, -5, 6, -8, 7, -9, 5 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 10 12 16 14 2 18 8 6 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [41112] |
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,−3,2,−3,4,−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, 3}, {2, 9}, {10, 4}, {3, 5}, {9, 11}, {4, 1}, {6, 2}, {5, 7}, {8, 6}, {7, 10}, {1, 8}] |
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 | 2t2−9t + 15−9t−1 + 2t−2 |
| Conway polynomial | 2z4−z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 37, 0 } |
| Jones polynomial | q6−2q5 + 3q4−5q3 + 6q2−6q + 6−4q−1 + 3q−2−q−3 |
| HOMFLY-PT polynomial (db, data sources) | z4a−2 + z4−a2z2 + z2a−2−2z2a−4 + z2 + a−2−2a−4 + a−6 + 1 |
| Kauffman polynomial (db, data sources) | z8a−2 + z8a−4 + 3z7a−1 + 5z7a−3 + 2z7a−5 + 3z6a−2 + z6a−6 + 4z6 + 4az5−4z5a−1−16z5a−3−8z5a−5 + 3a2z4−12z4a−2−9z4a−4−4z4a−6−4z4 + a3z3−3az3 + 2z3a−1 + 15z3a−3 + 9z3a−5−2a2z2 + 8z2a−2 + 10z2a−4 + 4z2a−6−2za−1−5za−3−3za−5−a−2−2a−4−a−6 + 1 |
| The A2 invariant | −q10 + q8 + q6−q4 + 2q2 + q−2 + q−4 + q−8−2q−10−q−12−q−16 + q−18 + q−20 |
| The G2 invariant | q52−2q50 + 3q48−4q46 + q44−3q40 + 8q38−10q36 + 11q34−8q32 + 2q30 + 4q28−10q26 + 16q24−16q22 + 14q20−8q18−q16 + 11q14−15q12 + 17q10−12q8 + 3q6 + 6q4−10q2 + 10−2q−2−6q−4 + 15q−6−16q−8 + 9q−10 + 5q−12−19q−14 + 30q−16−28q−18 + 18q−20−16q−24 + 28q−26−30q−28 + 23q−30−10q−32−6q−34 + 16q−36−19q−38 + 15q−40−5q−42−7q−44 + 11q−46−13q−48 + 5q−50 + 5q−52−16q−54 + 21q−56−19q−58 + 6q−60 + 8q−62−20q−64 + 25q−66−21q−68 + 11q−70 + q−72−10q−74 + 16q−76−14q−78 + 10q−80−2q−82−2q−84 + 3q−86−4q−88 + 3q−90−q−92 + q−94 |
Further Quantum Invariants
Further quantum knot invariants for 9_14.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | −q7 + 2q5−q3 + 2q + q−5−2q−7 + q−9−q−11 + q−13 |
| 2 | q20−2q18−q16 + 4q14−4q12 + 7q8−5q6−q4 + 7q2−3−3q−2 + 3q−4 + 2q−6−3q−8−2q−10 + 5q−12−q−14−6q−16 + 5q−18 + 2q−20−6q−22 + 4q−24 + 4q−26−5q−28 + 3q−32−2q−34−q−36 + q−38 |
| 3 | −q39 + 2q37 + q35−2q33−2q31 + q29 + 3q27−5q25 + 6q21−10q17 + 3q15 + 14q13−q11−17q9 + 19q5 + 5q3−16q−9q−1 + 10q−3 + 11q−5−2q−7−14q−9−3q−11 + 12q−13 + 10q−15−11q−17−13q−19 + 8q−21 + 16q−23−6q−25−16q−27 + 2q−29 + 18q−31 + 2q−33−17q−35−6q−37 + 16q−39 + 12q−41−13q−43−15q−45 + 5q−47 + 16q−49−q−51−14q−53−4q−55 + 10q−57 + 7q−59−5q−61−6q−63 + 2q−65 + 4q−67−2q−71−q−73 + q−75 |
| 4 | q64−2q62−q60 + 2q58 + 5q54−4q52−2q50−6q46 + 11q44−2q42 + 3q40−21q36 + 4q34 + 6q32 + 26q30 + 10q28−43q26−22q24 + 4q22 + 56q20 + 40q18−48q16−56q14−24q12 + 60q10 + 70q8−16q6−54q4−55q2 + 21 + 63q−2 + 24q−4−14q−6−52q−8−26q−10 + 19q−12 + 41q−14 + 30q−16−25q−18−48q−20−17q−22 + 41q−24 + 47q−26−3q−28−53q−30−36q−32 + 39q−34 + 51q−36 + 8q−38−57q−40−48q−42 + 34q−44 + 54q−46 + 29q−48−47q−50−64q−52 + 8q−54 + 45q−56 + 56q−58−14q−60−63q−62−29q−64 + 8q−66 + 62q−68 + 30q−70−28q−72−41q−74−34q−76 + 32q−78 + 44q−80 + 15q−82−17q−84−47q−86−6q−88 + 21q−90 + 27q−92 + 12q−94−25q−96−17q−98−4q−100 + 12q−102 + 16q−104−4q−106−6q−108−6q−110 + 6q−114 + q−116−2q−120−q−122 + q−124 |
| 5 | −q95 + 2q93 + q91−2q89−3q85−2q83 + 3q81 + 7q79 + 3q77−q75−8q73−12q71−4q69 + 13q67 + 26q65 + 10q63−15q61−36q59−38q57 + 9q55 + 66q53 + 62q51 + q49−80q47−112q45−33q43 + 111q41 + 167q39 + 71q37−114q35−226q33−137q31 + 104q29 + 277q27 + 209q25−60q23−298q21−276q19−8q17 + 276q15 + 324q13 + 90q11−216q9−326q7−162q5 + 119q3 + 282q + 208q−1−17q−3−202q−5−216q−7−66q−9 + 103q−11 + 184q−13 + 132q−15−13q−17−142q−19−158q−21−53q−23 + 90q−25 + 172q−27 + 104q−29−65q−31−169q−33−121q−35 + 46q−37 + 177q−39 + 134q−41−48q−43−189q−45−148q−47 + 46q−49 + 209q−51 + 168q−53−43q−55−223q−57−200q−59 + 18q−61 + 233q−63 + 234q−65 + 20q−67−213q−69−260q−71−80q−73 + 172q−75 + 272q−77 + 137q−79−105q−81−250q−83−190q−85 + 19q−87 + 202q−89 + 217q−91 + 59q−93−122q−95−199q−97−131q−99 + 32q−101 + 157q−103 + 159q−105 + 50q−107−79q−109−149q−111−112q−113 + 3q−115 + 104q−117 + 127q−119 + 61q−121−42q−123−107q−125−95q−127−16q−129 + 65q−131 + 93q−133 + 51q−135−18q−137−65q−139−62q−141−15q−143 + 34q−145 + 51q−147 + 27q−149−7q−151−29q−153−28q−155−6q−157 + 14q−159 + 17q−161 + 7q−163−2q−165−8q−167−8q−169 + 4q−173 + 3q−175 + q−177−2q−181−q−183 + q−185 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | −q10 + q8 + q6−q4 + 2q2 + q−2 + q−4 + q−8−2q−10−q−12−q−16 + q−18 + q−20 |
| 1,1 | q28−4q26 + 8q24−12q22 + 18q20−28q18 + 34q16−38q14 + 43q12−48q10 + 50q8−44q6 + 46q4−32q2 + 22−24q−4 + 50q−6−80q−8 + 102q−10−118q−12 + 126q−14−126q−16 + 108q−18−91q−20 + 62q−22−30q−24 + 34q−28−50q−30 + 70q−32−76q−34 + 71q−36−62q−38 + 48q−40−36q−42 + 21q−44−12q−46 + 6q−48−2q−50 + q−52 |
| 2,0 | q26−q24−2q22 + q20 + 2q18−q16−4q14 + 3q12 + 5q10−3q8−2q6 + 6q4 + 4q2−2−2q−2 + 2q−4−q−8 + q−10−3q−14 + 2q−16 + q−18−5q−20−3q−22 + 2q−24 + 3q−26−2q−28 + 5q−32 + 4q−34−2q−36−2q−38 + q−40 + q−42−2q−44−3q−46 + q−50 + q−52 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q22−2q20−q18 + 4q16−3q14−2q12 + 6q10−2q8−4q6 + 7q4 + q2−1 + 5q−2 + 2q−4−2q−6−3q−8−6q−14 + 2q−16 + 5q−18−4q−20 + 2q−22 + 4q−24−4q−26 + 2q−30−3q−32 + q−34 + q−36−q−38 + q−40 |
| 1,0,0 | −q13 + q11 + q7−q5 + 2q3 + q−1 + q−3 + q−5 + q−7 + q−11−2q−13−q−15−2q−17−q−21 + q−23 + q−25 + q−27 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | −q22 + 2q20−3q18 + 4q16−5q14 + 6q12−6q10 + 6q8−4q6 + 3q4 + q2−3 + 7q−2−8q−4 + 12q−6−11q−8 + 12q−10−10q−12 + 8q−14−6q−16 + q−18−4q−22 + 4q−24−6q−26 + 6q−28−6q−30 + 5q−32−3q−34 + 3q−36−q−38 + q−40 |
| 1,0 | q36−2q32−2q30 + q28 + 4q26 + q24−4q22−4q20 + 2q18 + 6q16 + 2q14−5q12−4q10 + 3q8 + 7q6−4q2 + 6q−2 + 3q−4−3q−6−4q−8 + 2q−10 + 3q−12−2q−14−5q−16 + 3q−20−q−22−5q−24−q−26 + 6q−28 + 4q−30−3q−32−6q−34 + 2q−36 + 7q−38 + 3q−40−5q−42−5q−44 + 2q−46 + 5q−48−4q−52−2q−54 + 2q−56 + 2q−58−q−60−q−62 + q−66 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q52−2q50 + 3q48−4q46 + q44−3q40 + 8q38−10q36 + 11q34−8q32 + 2q30 + 4q28−10q26 + 16q24−16q22 + 14q20−8q18−q16 + 11q14−15q12 + 17q10−12q8 + 3q6 + 6q4−10q2 + 10−2q−2−6q−4 + 15q−6−16q−8 + 9q−10 + 5q−12−19q−14 + 30q−16−28q−18 + 18q−20−16q−24 + 28q−26−30q−28 + 23q−30−10q−32−6q−34 + 16q−36−19q−38 + 15q−40−5q−42−7q−44 + 11q−46−13q−48 + 5q−50 + 5q−52−16q−54 + 21q−56−19q−58 + 6q−60 + 8q−62−20q−64 + 25q−66−21q−68 + 11q−70 + q−72−10q−74 + 16q−76−14q−78 + 10q−80−2q−82−2q−84 + 3q−86−4q−88 + 3q−90−q−92 + q−94 |
.
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 14"];
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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]=
| 2t2−9t + 15−9t−1 + 2t−2 |
In[5]:=
| Conway[K][z]
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Out[5]=
| 2z4−z2 + 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.
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Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
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Out[7]=
| { 37, 0 } |
In[8]:=
| Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
| q6−2q5 + 3q4−5q3 + 6q2−6q + 6−4q−1 + 3q−2−q−3 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| z4a−2 + z4−a2z2 + z2a−2−2z2a−4 + z2 + a−2−2a−4 + a−6 + 1 |
In[10]:=
| Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
| z8a−2 + z8a−4 + 3z7a−1 + 5z7a−3 + 2z7a−5 + 3z6a−2 + z6a−6 + 4z6 + 4az5−4z5a−1−16z5a−3−8z5a−5 + 3a2z4−12z4a−2−9z4a−4−4z4a−6−4z4 + a3z3−3az3 + 2z3a−1 + 15z3a−3 + 9z3a−5−2a2z2 + 8z2a−2 + 10z2a−4 + 4z2a−6−2za−1−5za−3−3za−5−a−2−2a−4−a−6 + 1 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, 
):
{K11n53,}
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 14"];
|
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]=
| { 2t2−9t + 15−9t−1 + 2t−2, q6−2q5 + 3q4−5q3 + 6q2−6q + 6−4q−1 + 3q−2−q−3 } |
In[5]:=
| DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
|
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.
|
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]=
| {K11n53,} |
[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 = 0 is the signature of 9 14. 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 | q18−2q17−q16 + 6q15−5q14−6q13 + 15q12−5q11−16q10 + 23q9−2q8−27q7 + 28q6 + 4q5−34q4 + 27q3 + 9q2−33q + 21 + 9q−1−23q−2 + 13q−3 + 5q−4−11q−5 + 6q−6 + q−7−3q−8 + q−9 |
| 3 | q36−2q35−q34 + 2q33 + 5q32−4q31−9q30 + 3q29 + 17q28−q27−23q26−7q25 + 30q24 + 16q23−34q22−27q21 + 32q20 + 41q19−30q18−49q17 + 21q16 + 60q15−14q14−65q13 + 3q12 + 70q11 + 8q10−73q9−18q8 + 72q7 + 29q6−71q5−33q4 + 61q3 + 41q2−58q−34 + 42q−1 + 34q−2−37q−3−20q−4 + 23q−5 + 17q−6−21q−7−5q−8 + 12q−9 + 4q−10−11q−11 + q−12 + 6q−13−q−14−3q−15−q−16 + 3q−17−q−18 |
| 4 | q60−2q59−q58 + 2q57 + q56 + 6q55−8q54−7q53 + 2q52 + 3q51 + 26q50−12q49−23q48−11q47−5q46 + 63q45 + 3q44−29q43−38q42−46q41 + 93q40 + 35q39−50q37−112q36 + 86q35 + 48q34 + 58q33−18q32−166q31 + 49q30 + 14q29 + 107q28 + 52q27−177q26 + 12q25−58q24 + 124q23 + 128q22−152q21−8q20−140q19 + 115q18 + 193q17−109q16−20q15−215q14 + 98q13 + 243q12−59q11−26q10−273q9 + 67q8 + 266q7−4q6−15q5−295q4 + 22q3 + 240q2 + 34q + 23−256q−1−20q−2 + 164q−3 + 35q−4 + 61q−5−170q−6−30q−7 + 80q−8 + 3q−9 + 69q−10−82q−11−14q−12 + 28q−13−23q−14 + 48q−15−29q−16 + 2q−17 + 8q−18−25q−19 + 23q−20−8q−21 + 5q−22 + 3q−23−12q−24 + 6q−25−2q−26 + 3q−27 + q−28−3q−29 + q−30 |
| 5 | q90−2q89−q88 + 2q87 + q86 + 2q85 + 2q84−6q83−9q82 + 2q81 + 7q80 + 11q79 + 12q78−9q77−29q76−20q75 + 6q74 + 33q73 + 46q72 + 15q71−46q70−69q69−41q68 + 30q67 + 93q66 + 84q65−4q64−97q63−122q62−49q61 + 81q60 + 149q59 + 99q58−31q57−145q56−150q55−34q54 + 112q53 + 169q52 + 98q51−36q50−152q49−159q48−51q47 + 101q46 + 175q45 + 145q44 + 6q43−174q42−234q41−108q40 + 115q39 + 290q38 + 248q37−39q36−334q35−360q34−65q33 + 337q32 + 481q31 + 175q30−335q29−575q28−283q27 + 314q26 + 661q25 + 386q24−294q23−738q22−477q21 + 273q20 + 802q19 + 568q18−251q17−869q16−644q15 + 225q14 + 906q13 + 737q12−183q11−951q10−787q9 + 120q8 + 922q7 + 866q6−38q5−899q4−868q3−49q2 + 772q + 880 + 147q−1−674q−2−794q−3−212q−4 + 491q−5 + 716q−6 + 257q−7−368q−8−560q−9−260q−10 + 207q−11 + 448q−12 + 235q−13−130q−14−291q−15−192q−16 + 34q−17 + 207q−18 + 146q−19−18q−20−106q−21−96q−22−22q−23 + 63q−24 + 67q−25 + 14q−26−25q−27−35q−28−18q−29 + 6q−30 + 20q−31 + 16q−32−4q−33−10q−34−2q−35−7q−36 + 3q−37 + 8q−38−3q−40 + 2q−41−3q−42−q−43 + 3q−44−q−45 |
| 6 | q126−2q125−q124 + 2q123 + q122 + 2q121−2q120 + 4q119−8q118−9q117 + 5q116 + 6q115 + 12q114 + 16q112−22q111−35q110−9q109 + 5q108 + 36q107 + 21q106 + 70q105−21q104−79q103−68q102−48q101 + 30q100 + 43q99 + 193q98 + 62q97−60q96−133q95−165q94−86q93−49q92 + 295q91 + 209q90 + 108q89−57q88−200q87−245q86−311q85 + 201q84 + 214q83 + 285q82 + 170q81 + 27q80−189q79−516q78−37q77−79q76 + 170q75 + 243q74 + 381q73 + 195q72−341q71−51q70−447q69−301q68−148q67 + 447q66 + 615q65 + 212q64 + 436q63−453q62−784q61−930q60−15q59 + 645q58 + 765q57 + 1296q56 + 92q55−879q54−1711q53−848q52 + 151q51 + 960q50 + 2146q49 + 1001q48−494q47−2172q46−1702q45−668q44 + 748q43 + 2720q42 + 1943q41 + 167q40−2283q39−2349q38−1514q37 + 326q36 + 3007q35 + 2713q34 + 832q33−2217q32−2784q31−2212q30−69q29 + 3160q28 + 3299q27 + 1356q26−2150q25−3128q24−2763q23−352q22 + 3297q21 + 3795q20 + 1786q19−2085q18−3443q17−3262q16−644q15 + 3332q14 + 4210q13 + 2258q12−1817q11−3570q10−3697q9−1116q8 + 3007q7 + 4328q6 + 2736q5−1174q4−3219q3−3810q2−1684q + 2192 + 3857q−1 + 2909q−2−334q−3−2323q−4−3321q−5−1975q−6 + 1165q−7 + 2814q−8 + 2515q−9 + 269q−10−1243q−11−2327q−12−1750q−13 + 391q−14 + 1636q−15 + 1707q−16 + 415q−17−438q−18−1290q−19−1195q−20 + 47q−21 + 765q−22 + 919q−23 + 276q−24−49q−25−574q−26−664q−27−20q−28 + 291q−29 + 409q−30 + 117q−31 + 64q−32−207q−33−323q−34−9q−35 + 87q−36 + 155q−37 + 33q−38 + 67q−39−58q−40−139q−41 + q−42 + 14q−43 + 50q−44 + 2q−45 + 41q−46−11q−47−49q−48 + 4q−49−3q−50 + 14q−51−5q−52 + 17q−53−q−54−14q−55 + 4q−56−3q−57 + 3q−58−2q−59 + 3q−60 + q−61−3q−62 + q−63 |
[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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