9 39
From Knot Atlas
|
|
|
|
 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 9 39's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9_39's page at Knotilus! Visit 9 39's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X1627 X3,11,4,10 X7,18,8,1 X17,13,18,12 X9,17,10,16 X5,15,6,14 X15,5,16,4 X11,3,12,2 X13,9,14,8 |
| Gauss code | -1, 8, -2, 7, -6, 1, -3, 9, -5, 2, -8, 4, -9, 6, -7, 5, -4, 3 |
| Dowker-Thistlethwaite code | 6 10 14 18 16 2 8 4 12 |
| Conway Notation | [2:2:20] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 | 
|  [{11, 6}, {2, 7}, {6, 1}, {8, 3}, {5, 2}, {7, 9}, {4, 8}, {10, 5}, {9, 11}, {3, 10}, {1, 4}] |
[edit Notes on presentations of 9 39]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["9 39"];
|
In[4]:=
| PD[K]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| X1627 X3,11,4,10 X7,18,8,1 X17,13,18,12 X9,17,10,16 X5,15,6,14 X15,5,16,4 X11,3,12,2 X13,9,14,8 |
In[5]:=
| GaussCode[K]
|
Out[5]=
| -1, 8, -2, 7, -6, 1, -3, 9, -5, 2, -8, 4, -9, 6, -7, 5, -4, 3 |
In[6]:=
| DTCode[K]
|
Out[6]=
| 6 10 14 18 16 2 8 4 12 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
|
In[8]:=
| ConwayNotation[K]
|
Out[8]=
| [2:2:20] |
In[9]:=
| br = BR[K]
|
KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
|
Out[9]=
| BR(5,{1,1,2,−1,−3,−2,1,4,3,−2,3,4}) |
In[10]:=
| {First[br], Crossings[br], BraidIndex[K]}
|
KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
|
KnotTheory::loading: Loading precomputed data in IndianaData`.
|
Out[10]=
| { 5, 12, 5 } |
In[11]:=
| Show[BraidPlot[br]]
|
|
Out[11]=
| -Graphics- |
In[12]:=
| Show[DrawMorseLink[K]]
|
KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
|
KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
|
|
|
Out[12]=
| -Graphics- |
In[13]:=
| ap = ArcPresentation[K]
|
Out[13]=
| ArcPresentation[{11, 6}, {2, 7}, {6, 1}, {8, 3}, {5, 2}, {7, 9}, {4, 8}, {10, 5}, {9, 11}, {3, 10}, {1, 4}] |
In[14]:=
| Draw[ap]
|
|
|
Out[14]=
| -Graphics- |
[edit] Three dimensional invariants
|
[edit] Four dimensional invariants
|
[edit] Polynomial invariants
| Alexander polynomial | −3t2 + 14t−21 + 14t−1−3t−2 |
| Conway polynomial | −3z4 + 2z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 55, 2 } |
| Jones polynomial | −q8 + 3q7−6q6 + 8q5−9q4 + 10q3−8q2 + 6q−3 + q−1 |
| HOMFLY-PT polynomial (db, data sources) | −z4a−2−2z4a−4 + z2a−2−3z2a−4 + 3z2a−6 + z2 + 2a−2−2a−4 + 2a−6−a−8 |
| Kauffman polynomial (db, data sources) | 2z8a−4 + 2z8a−6 + 5z7a−3 + 9z7a−5 + 4z7a−7 + 5z6a−2 + 5z6a−4 + 3z6a−6 + 3z6a−8 + 3z5a−1−7z5a−3−18z5a−5−7z5a−7 + z5a−9−7z4a−2−15z4a−4−13z4a−6−6z4a−8 + z4−3z3a−1 + 5z3a−3 + 12z3a−5 + 2z3a−7−2z3a−9 + 5z2a−2 + 12z2a−4 + 9z2a−6 + 3z2a−8−z2−za−3−3za−5−za−7 + za−9−2a−2−2a−4−2a−6−a−8 |
| The A2 invariant | q4−q2−1 + 3q−2−q−4 + 2q−6 + q−8−q−10 + q−12−2q−14 + 2q−16−q−20 + 2q−22−q−24−q−26 |
| The G2 invariant | q18−2q16 + 4q14−6q12 + 5q10−3q8−2q6 + 12q4−19q2 + 28−30q−2 + 21q−4−3q−6−27q−8 + 58q−10−76q−12 + 73q−14−45q−16−6q−18 + 63q−20−97q−22 + 101q−24−61q−26 + 2q−28 + 53q−30−80q−32 + 65q−34−12q−36−45q−38 + 87q−40−83q−42 + 36q−44 + 37q−46−103q−48 + 134q−50−123q−52 + 66q−54 + 10q−56−84q−58 + 131q−60−134q−62 + 95q−64−29q−66−43q−68 + 87q−70−93q−72 + 59q−74−52q−78 + 80q−80−61q−82 + 8q−84 + 57q−86−100q−88 + 103q−90−65q−92−q−94 + 60q−96−93q−98 + 95q−100−63q−102 + 19q−104 + 19q−106−45q−108 + 45q−110−33q−112 + 17q−114−3q−116−6q−118 + 8q−120−8q−122 + 5q−124−2q−126 + q−128 |
Further Quantum Invariants
Further quantum knot invariants for 9_39.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q3−2q + 3q−1−2q−3 + 2q−5 + q−7−q−9 + 2q−11−3q−13 + 2q−15−q−17 |
| 2 | q10−2q8 + 6q4−8q2−3 + 18q−2−10q−4−13q−6 + 21q−8−2q−10−15q−12 + 11q−14 + 7q−16−7q−18−6q−20 + 11q−22 + 2q−24−18q−26 + 10q−28 + 12q−30−20q−32 + 2q−34 + 16q−36−11q−38−5q−40 + 8q−42−q−44−2q−46 + q−48 |
| 3 | q21−2q19 + 3q15−7q11−q9 + 19q7 + 4q5−35q3−18q + 50q−1 + 49q−3−58q−5−81q−7 + 48q−9 + 110q−11−22q−13−124q−15−8q−17 + 120q−19 + 35q−21−92q−23−56q−25 + 63q−27 + 66q−29−28q−31−69q−33−7q−35 + 70q−37 + 34q−39−68q−41−65q−43 + 66q−45 + 87q−47−51q−49−109q−51 + 28q−53 + 119q−55 + 3q−57−116q−59−33q−61 + 92q−63 + 58q−65−59q−67−66q−69 + 28q−71 + 54q−73−35q−77−11q−79 + 17q−81 + 8q−83−5q−85−4q−87 + q−89 + 2q−91−q−93 |
| 4 | q36−2q34 + 3q30−3q28 + q26−5q24 + 7q22 + 16q20−16q18−18q16−29q14 + 34q12 + 94q10 + 4q8−88q6−177q4−4q2 + 269 + 223q−2−46q−4−458q−6−324q−8 + 281q−10 + 587q−12 + 333q−14−510q−16−757q−18−93q−20 + 656q−22 + 779q−24−153q−26−823q−28−512q−30 + 308q−32 + 823q−34 + 256q−36−471q−38−598q−40−94q−42 + 514q−44 + 420q−46−67q−48−446q−50−319q−52 + 170q−54 + 444q−56 + 222q−58−308q−60−471q−62−86q−64 + 492q−66 + 480q−68−189q−70−631q−72−374q−74 + 475q−76 + 743q−78 + 71q−80−654q−82−709q−84 + 199q−86 + 807q−88 + 460q−90−333q−92−826q−94−250q−96 + 475q−98 + 623q−100 + 160q−102−511q−104−453q−106−18q−108 + 365q−110 + 359q−112−71q−114−252q−116−199q−118 + 31q−120 + 191q−122 + 81q−124−19q−126−92q−128−50q−130 + 31q−132 + 27q−134 + 19q−136−11q−138−14q−140 + 2q−142 + q−144 + 4q−146−q−148−2q−150 + q−152 |
| 5 | q55−2q53 + 3q49−3q47−2q45 + 3q43 + 3q41 + 4q39 + 3q37−16q35−28q33 + q31 + 45q29 + 67q27 + 26q25−78q23−176q21−133q19 + 107q17 + 362q15 + 373q13−4q11−574q9−844q7−376q5 + 690q3 + 1486q + 1143q−1−420q−3−2090q−5−2322q−7−436q−9 + 2359q−11 + 3622q−13 + 1876q−15−1907q−17−4647q−19−3684q−21 + 702q−23 + 4997q−25 + 5332q−27 + 1068q−29−4429q−31−6381q−33−2940q−35 + 3094q−37 + 6539q−39 + 4408q−41−1367q−43−5793q−45−5162q−47−316q−49 + 4443q−51 + 5172q−53 + 1581q−55−2899q−57−4539q−59−2348q−61 + 1461q−63 + 3655q−65 + 2656q−67−365q−69−2756q−71−2693q−73−426q−75 + 2053q−77 + 2705q−79 + 986q−81−1633q−83−2831q−85−1472q−87 + 1364q−89 + 3173q−91 + 2078q−93−1183q−95−3652q−97−2847q−99 + 821q−101 + 4136q−103 + 3841q−105−172q−107−4404q−109−4877q−111−889q−113 + 4209q−115 + 5774q−117 + 2249q−119−3374q−121−6210q−123−3713q−125 + 1949q−127 + 5923q−129 + 4882q−131−119q−133−4818q−135−5431q−137−1681q−139 + 3105q−141 + 5089q−143 + 2990q−145−1136q−147−3955q−149−3519q−151−540q−153 + 2391q−155 + 3163q−157 + 1561q−159−845q−161−2237q−163−1830q−165−226q−167 + 1171q−169 + 1467q−171 + 718q−173−315q−175−884q−177−723q−179−124q−181 + 366q−183 + 470q−185 + 238q−187−59q−189−223q−191−183q−193−32q−195 + 70q−197 + 84q−199 + 39q−201−7q−203−33q−205−22q−207 + 3q−209 + 8q−211 + 4q−213 + 2q−215−q−217−4q−219 + q−221 + 2q−223−q−225 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q4−q2−1 + 3q−2−q−4 + 2q−6 + q−8−q−10 + q−12−2q−14 + 2q−16−q−20 + 2q−22−q−24−q−26 |
| 1,1 | q12−4q10 + 10q8−20q6 + 38q4−62q2 + 98−150q−2 + 211q−4−270q−6 + 334q−8−374q−10 + 372q−12−316q−14 + 212q−16−54q−18−136q−20 + 344q−22−522q−24 + 662q−26−745q−28 + 754q−30−702q−32 + 582q−34−415q−36 + 218q−38−18q−40−158q−42 + 298q−44−386q−46 + 410q−48−380q−50 + 319q−52−248q−54 + 168q−56−102q−58 + 58q−60−28q−62 + 12q−64−4q−66 + q−68 |
| 2,0 | q12−q10−2q8 + 2q6 + 5q4−q2−10 + 14q−4−11q−8 + 3q−10 + 11q−12−q−14−10q−16 + 3q−18 + 6q−20−3q−22 + 2q−24 + 3q−26−2q−28 + 8q−32−5q−34−10q−36 + 2q−38 + 9q−40−4q−42−12q−44 + 6q−46 + 9q−48−2q−50−8q−52 + 6q−56−3q−60−q−62 + q−64 + q−66 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q8−2q6 + 5q2−6−q−2 + 13q−4−10q−6−3q−8 + 17q−10−10q−12−4q−14 + 12q−16−4q−18−3q−20 + 2q−22 + 5q−24−2q−26−8q−28 + 8q−30 + 4q−32−15q−34 + 9q−36 + 7q−38−15q−40 + 7q−42 + 3q−44−8q−46 + 4q−48 + q−50−2q−52 + q−54 |
| 1,0,0 | q5−q3−q−1 + 3q−3−q−5 + 3q−7 + q−9 + q−11−q−13−q−15−2q−19 + 2q−21 + 2q−25−q−27 + 2q−29−q−31−q−33−q−35 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | q8−2q6 + 4q4−7q2 + 10−13q−2 + 17q−4−16q−6 + 15q−8−9q−10 + 4q−12 + 4q−14−12q−16 + 20q−18−27q−20 + 30q−22−31q−24 + 28q−26−22q−28 + 16q−30−6q−32−q−34 + 9q−36−13q−38 + 15q−40−17q−42 + 15q−44−12q−46 + 8q−48−5q−50 + 2q−52−q−54 |
| 1,0 | q14−2q10−2q8 + 2q6 + 6q4 + q2−8−7q−2 + 6q−4 + 15q−6 + q−8−16q−10−9q−12 + 13q−14 + 15q−16−5q−18−16q−20 + 15q−24 + 5q−26−12q−28−6q−30 + 10q−32 + 9q−34−6q−36−10q−38 + 4q−40 + 11q−42−2q−44−12q−46−2q−48 + 13q−50 + 6q−52−13q−54−14q−56 + 9q−58 + 18q−60−q−62−17q−64−8q−66 + 12q−68 + 11q−70−5q−72−10q−74−q−76 + 6q−78 + 3q−80−2q−82−2q−84 + q−88 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q18−2q16 + 4q14−6q12 + 5q10−3q8−2q6 + 12q4−19q2 + 28−30q−2 + 21q−4−3q−6−27q−8 + 58q−10−76q−12 + 73q−14−45q−16−6q−18 + 63q−20−97q−22 + 101q−24−61q−26 + 2q−28 + 53q−30−80q−32 + 65q−34−12q−36−45q−38 + 87q−40−83q−42 + 36q−44 + 37q−46−103q−48 + 134q−50−123q−52 + 66q−54 + 10q−56−84q−58 + 131q−60−134q−62 + 95q−64−29q−66−43q−68 + 87q−70−93q−72 + 59q−74−52q−78 + 80q−80−61q−82 + 8q−84 + 57q−86−100q−88 + 103q−90−65q−92−q−94 + 60q−96−93q−98 + 95q−100−63q−102 + 19q−104 + 19q−106−45q−108 + 45q−110−33q−112 + 17q−114−3q−116−6q−118 + 8q−120−8q−122 + 5q−124−2q−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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
| K = Knot["9 39"];
|
In[4]:=
| Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| −3t2 + 14t−21 + 14t−1−3t−2 |
In[5]:=
| Conway[K][z]
|
Out[5]=
| −3z4 + 2z2 + 1 |
In[6]:=
| Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
|
Out[7]=
| { 55, 2 } |
In[8]:=
| Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
| −q8 + 3q7−6q6 + 8q5−9q4 + 10q3−8q2 + 6q−3 + q−1 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| −z4a−2−2z4a−4 + z2a−2−3z2a−4 + 3z2a−6 + z2 + 2a−2−2a−4 + 2a−6−a−8 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| 2z8a−4 + 2z8a−6 + 5z7a−3 + 9z7a−5 + 4z7a−7 + 5z6a−2 + 5z6a−4 + 3z6a−6 + 3z6a−8 + 3z5a−1−7z5a−3−18z5a−5−7z5a−7 + z5a−9−7z4a−2−15z4a−4−13z4a−6−6z4a−8 + z4−3z3a−1 + 5z3a−3 + 12z3a−5 + 2z3a−7−2z3a−9 + 5z2a−2 + 12z2a−4 + 9z2a−6 + 3z2a−8−z2−za−3−3za−5−za−7 + za−9−2a−2−2a−4−2a−6−a−8 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11n162,}
Same Jones Polynomial (up to mirroring, 
):
{K11n11, K11n112,}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["9 39"];
|
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]=
| { −3t2 + 14t−21 + 14t−1−3t−2, −q8 + 3q7−6q6 + 8q5−9q4 + 10q3−8q2 + 6q−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]=
| {K11n162,} |
In[6]:=
| DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
| {K11n11, K11n112,} |
[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 39. 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 | q23−3q22 + q21 + 10q20−16q19−5q18 + 37q17−30q16−27q15 + 69q14−32q13−55q12 + 89q11−23q10−72q9 + 88q8−9q7−68q6 + 62q5 + 4q4−45q3 + 28q2 + 7q−17 + 7q−1 + 2q−2−3q−3 + q−4 |
| 3 | −q45 + 3q44−q43−5q42−2q41 + 16q40 + 8q39−33q38−26q37 + 51q36 + 62q35−59q34−120q33 + 58q32 + 179q31−25q30−245q29−25q28 + 298q27 + 91q26−336q25−162q24 + 356q23 + 229q22−357q21−293q20 + 353q19 + 331q18−321q17−370q16 + 291q15 + 372q14−227q13−373q12 + 172q11 + 336q10−100q9−288q8 + 44q7 + 220q6 + 2q5−156q4−18q3 + 91q2 + 25q−49−17q−1 + 23q−2 + 8q−3−10q−4−2q−5 + 3q−6 + 2q−7−3q−8 + q−9 |
| 4 | q74−3q73 + q72 + 5q71−3q70 + 2q69−19q68 + 4q67 + 35q66 + 5q65 + 6q64−100q63−38q62 + 108q61 + 105q60 + 116q59−260q58−268q57 + 55q56 + 286q55 + 546q54−254q53−651q52−380q51 + 228q50 + 1217q49 + 209q48−799q47−1105q46−348q45 + 1710q44 + 1002q43−452q42−1713q41−1256q40 + 1765q39 + 1727q38 + 220q37−1981q36−2105q35 + 1508q34 + 2169q33 + 889q32−1969q31−2683q30 + 1123q29 + 2332q28 + 1419q27−1747q26−2957q25 + 634q24 + 2205q23 + 1798q22−1260q21−2863q20 + 26q19 + 1701q18 + 1925q17−533q16−2296q15−489q14 + 881q13 + 1614q12 + 137q11−1364q10−612q9 + 132q8 + 950q7 + 384q6−521q5−358q4−174q3 + 345q2 + 250q−109−89q−1−128q−2 + 72q−3 + 77q−4−20q−5 + 3q−6−38q−7 + 12q−8 + 14q−9−9q−10 + 5q−11−6q−12 + 3q−13 + 2q−14−3q−15 + q−16 |
| 5 | −q110 + 3q109−q108−5q107 + 3q106 + 3q105 + q104 + 7q103−6q102−30q101−8q100 + 29q99 + 47q98 + 52q97−20q96−132q95−159q94−11q93 + 211q92 + 349q91 + 212q90−236q89−649q88−610q87 + 50q86 + 918q85 + 1245q84 + 513q83−945q82−2007q81−1554q80 + 511q79 + 2637q78 + 2919q77 + 657q76−2779q75−4485q74−2468q73 + 2201q72 + 5738q71 + 4783q70−680q69−6469q68−7254q67−1549q66 + 6351q65 + 9482q64 + 4321q63−5428q62−11228q61−7211q60 + 3854q59 + 12318q58 + 9944q57−1903q56−12793q55−12309q54−134q53 + 12791q52 + 14176q51 + 2110q50−12498q49−15624q48−3802q47 + 11986q46 + 16645q45 + 5371q44−11403q43−17433q42−6638q41 + 10627q40 + 17843q39 + 7990q38−9684q37−18085q36−9117q35 + 8360q34 + 17780q33 + 10381q32−6663q31−17086q30−11311q29 + 4551q28 + 15589q27 + 12021q26−2183q25−13495q24−12040q23−208q22 + 10743q21 + 11390q20 + 2243q19−7720q18−9909q17−3653q16 + 4709q15 + 7949q14 + 4195q13−2223q12−5645q11−3988q10 + 414q9 + 3563q8 + 3232q7 + 517q6−1862q5−2242q4−849q3 + 768q2 + 1346q + 749−192q−1−679q−2−506q−3−28q−4 + 280q−5 + 281q−6 + 78q−7−109q−8−129q−9−39q−10 + 25q−11 + 41q−12 + 35q−13−11q−14−25q−15 + 2q−16 + 3q−17−3q−18 + 6q−19 + q−20−6q−21 + 3q−22 + 2q−23−3q−24 + q−25 |
[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. |
|
