10 50
From Knot Atlas
|
|
|
|
 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 50's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_50's page at Knotilus! Visit 10 50's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X6271 X8493 X2837 X16,10,17,9 X14,5,15,6 X4,15,5,16 X20,14,1,13 X10,20,11,19 X18,12,19,11 X12,18,13,17 |
| Gauss code | 1, -3, 2, -6, 5, -1, 3, -2, 4, -8, 9, -10, 7, -5, 6, -4, 10, -9, 8, -7 |
| Dowker-Thistlethwaite code | 6 8 14 2 16 18 20 4 12 10 |
| Conway Notation | [32,3,2] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 | 
|  [{2, 12}, {1, 11}, {12, 10}, {11, 7}, {9, 4}, {10, 8}, {5, 3}, {4, 6}, {7, 5}, {6, 2}, {3, 9}, {8, 1}] |
[edit Notes on presentations of 10 50]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 50"];
|
In[4]:=
| PD[K]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| X6271 X8493 X2837 X16,10,17,9 X14,5,15,6 X4,15,5,16 X20,14,1,13 X10,20,11,19 X18,12,19,11 X12,18,13,17 |
In[5]:=
| GaussCode[K]
|
Out[5]=
| 1, -3, 2, -6, 5, -1, 3, -2, 4, -8, 9, -10, 7, -5, 6, -4, 10, -9, 8, -7 |
In[6]:=
| DTCode[K]
|
Out[6]=
| 6 8 14 2 16 18 20 4 12 10 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
|
In[8]:=
| ConwayNotation[K]
|
Out[8]=
| [32,3,2] |
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(4,{1,1,2,−1,2,2,−3,2,2,2,−3}) |
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]=
| { 4, 11, 4 } |
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[{2, 12}, {1, 11}, {12, 10}, {11, 7}, {9, 4}, {10, 8}, {5, 3}, {4, 6}, {7, 5}, {6, 2}, {3, 9}, {8, 1}] |
In[14]:=
| Draw[ap]
|
|
|
Out[14]=
| -Graphics- |
[edit] Three dimensional invariants
|
[edit] Four dimensional invariants
|
[edit] Polynomial invariants
| Alexander polynomial | −2t3 + 7t2−11t + 13−11t−1 + 7t−2−2t−3 |
| Conway polynomial | −2z6−5z4−z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 53, 4 } |
| Jones polynomial | q10−2q9 + 4q8−7q7 + 8q6−9q5 + 8q4−6q3 + 5q2−2q + 1 |
| HOMFLY-PT polynomial (db, data sources) | −z6a−4−z6a−6 + z4a−2−3z4a−4−4z4a−6 + z4a−8 + 3z2a−2−z2a−4−6z2a−6 + 3z2a−8 + 2a−2 + a−4−4a−6 + 2a−8 |
| Kauffman polynomial (db, data sources) | z9a−5 + z9a−7 + 2z8a−4 + 5z8a−6 + 3z8a−8 + 2z7a−3 + z7a−5 + 3z7a−7 + 4z7a−9 + z6a−2−4z6a−4−15z6a−6−7z6a−8 + 3z6a−10−6z5a−3−8z5a−5−15z5a−7−11z5a−9 + 2z5a−11−4z4a−2−z4a−4 + 18z4a−6 + 9z4a−8−5z4a−10 + z4a−12 + 3z3a−3 + 6z3a−5 + 22z3a−7 + 16z3a−9−3z3a−11 + 5z2a−2−13z2a−6−3z2a−8 + 3z2a−10−2z2a−12 + za−3−3za−5−10za−7−6za−9−2a−2 + a−4 + 4a−6 + 2a−8 |
| The A2 invariant | 1 + q−4 + 2q−6 + 3q−10−q−12−q−16−3q−18−2q−22 + q−24 + q−26 + q−30 |
| The G2 invariant | q−2−q−4 + 4q−6−5q−8 + 6q−10−3q−12−2q−14 + 12q−16−18q−18 + 25q−20−23q−22 + 11q−24 + 9q−26−30q−28 + 49q−30−48q−32 + 36q−34−7q−36−25q−38 + 51q−40−55q−42 + 41q−44−8q−46−22q−48 + 41q−50−37q−52 + 15q−54 + 17q−56−40q−58 + 46q−60−32q−62−q−64 + 35q−66−64q−68 + 68q−70−53q−72 + 15q−74 + 23q−76−62q−78 + 71q−80−64q−82 + 32q−84 + 4q−86−40q−88 + 51q−90−43q−92 + 16q−94 + 15q−96−34q−98 + 34q−100−14q−102−12q−104 + 38q−106−43q−108 + 38q−110−13q−112−13q−114 + 35q−116−42q−118 + 41q−120−24q−122 + 6q−124 + 10q−126−21q−128 + 23q−130−22q−132 + 16q−134−7q−136−q−138 + 6q−140−10q−142 + 9q−144−7q−146 + 5q−148−2q−150−q−152 + 2q−154−3q−156 + 2q−158−q−160 + q−162 |
Further Quantum Invariants
Further quantum knot invariants for 10_50.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q−q−1 + 3q−3−q−5 + 2q−7−q−9−q−11 + q−13−3q−15 + 2q−17−q−19 + q−21 |
| 2 | q6−q4−q2 + 5−q−2−6q−4 + 9q−6 + 3q−8−11q−10 + 6q−12 + 8q−14−12q−16−q−18 + 9q−20−6q−22−5q−24 + 6q−26 + 3q−28−7q−30−2q−32 + 12q−34−5q−36−8q−38 + 13q−40−2q−42−8q−44 + 6q−46−4q−50 + 2q−52−q−56 + q−58 |
| 3 | q15−q13−q11 + q9 + 4q7−q5−7q3 + 13q−1 + 5q−3−15q−5−15q−7 + 19q−9 + 25q−11−10q−13−36q−15−2q−17 + 41q−19 + 18q−21−39q−23−34q−25 + 28q−27 + 44q−29−16q−31−51q−33 + 6q−35 + 49q−37 + 9q−39−47q−41−14q−43 + 37q−45 + 23q−47−29q−49−27q−51 + 14q−53 + 35q−55 + 3q−57−38q−59−21q−61 + 37q−63 + 35q−65−30q−67−47q−69 + 18q−71 + 49q−73−9q−75−39q−77−5q−79 + 31q−81 + 9q−83−16q−85−9q−87 + 8q−89 + 6q−91−3q−93−3q−95 + q−97 + q−99−q−101−q−109 + q−111 |
| 4 | q28−q26−q24 + q22 + 4q18−3q16−5q14 + 2q12 + 2q10 + 15q8−5q6−19q4−9q2 + 1 + 45q−2 + 18q−4−26q−6−48q−8−47q−10 + 60q−12 + 81q−14 + 35q−16−55q−18−142q−20−25q−22 + 90q−24 + 152q−26 + 61q−28−160q−30−167q−32−43q−34 + 175q−36 + 226q−38−19q−40−206q−42−221q−44 + 53q−46 + 280q−48 + 152q−50−112q−52−287q−54−89q−56 + 210q−58 + 222q−60−8q−62−241q−64−144q−66 + 118q−68 + 203q−70 + 43q−72−163q−74−147q−76 + 38q−78 + 170q−80 + 87q−82−79q−84−159q−86−74q−88 + 122q−90 + 167q−92 + 61q−94−158q−96−226q−98 + 7q−100 + 211q−102 + 234q−104−59q−106−306q−108−155q−110 + 124q−112 + 311q−114 + 98q−116−217q−118−218q−120−36q−122 + 208q−124 + 164q−126−50q−128−135q−130−105q−132 + 56q−134 + 100q−136 + 29q−138−25q−140−66q−142−8q−144 + 27q−146 + 20q−148 + 11q−150−22q−152−6q−154 + 3q−156 + 3q−158 + 8q−160−7q−162−q−164 + q−166−q−168 + 3q−170−2q−172−q−178 + q−180 |
| 5 | q45−q43−q41 + q39 + 2q33−q31−4q29 + 2q27 + 5q25 + 2q23 + q21−8q19−15q17−6q15 + 19q13 + 31q11 + 23q9−11q7−55q5−64q3−18q + 64q−1 + 121q−3 + 88q−5−30q−7−157q−9−196q−11−83q−13 + 147q−15 + 299q−17 + 246q−19−6q−21−321q−23−453q−25−237q−27 + 210q−29 + 562q−31 + 549q−33 + 97q−35−519q−37−818q−39−510q−41 + 247q−43 + 913q−45 + 948q−47 + 221q−49−778q−51−1256q−53−769q−55 + 403q−57 + 1343q−59 + 1261q−61 + 123q−63−1189q−65−1581q−67−666q−69 + 842q−71 + 1674q−73 + 1095q−75−413q−77−1554q−79−1354q−81 + 7q−83 + 1318q−85 + 1403q−87 + 279q−89−1000q−91−1322q−93−445q−95 + 747q−97 + 1143q−99 + 476q−101−530q−103−958q−105−470q−107 + 411q−109 + 820q−111 + 441q−113−301q−115−740q−117−492q−119 + 189q−121 + 703q−123 + 629q−125 + 8q−127−670q−129−841q−131−316q−133 + 553q−135 + 1076q−137 + 740q−139−316q−141−1239q−143−1196q−145−88q−147 + 1233q−149 + 1609q−151 + 596q−153−1027q−155−1838q−157−1097q−159 + 604q−161 + 1810q−163 + 1484q−165−83q−167−1535q−169−1622q−171−389q−173 + 1037q−175 + 1519q−177 + 730q−179−535q−181−1193q−183−829q−185 + 90q−187 + 780q−189 + 754q−191 + 173q−193−400q−195−552q−197−273q−199 + 130q−201 + 334q−203 + 250q−205 + 17q−207−164q−209−179q−211−62q−213 + 60q−215 + 100q−217 + 60q−219−11q−221−50q−223−41q−225−2q−227 + 23q−229 + 19q−231 + 4q−233−6q−235−12q−237−2q−239 + 8q−241 + 2q−243−2q−245−2q−249−q−251 + 3q−253 + q−255−2q−257−q−263 + q−265 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | 1 + q−4 + 2q−6 + 3q−10−q−12−q−16−3q−18−2q−22 + q−24 + q−26 + q−30 |
| 1,1 | q4−2q2 + 8−16q−2 + 33q−4−48q−6 + 82q−8−110q−10 + 145q−12−164q−14 + 184q−16−178q−18 + 141q−20−94q−22 + 16q−24 + 62q−26−158q−28 + 228q−30−288q−32 + 326q−34−333q−36 + 312q−38−262q−40 + 202q−42−121q−44 + 46q−46 + 30q−48−80q−50 + 121q−52−140q−54 + 134q−56−128q−58 + 111q−60−94q−62 + 70q−64−56q−66 + 48q−68−34q−70 + 24q−72−18q−74 + 13q−76−8q−78 + 4q−80−2q−82 + q−84 |
| 2,0 | q4−1 + q−2 + 4q−4 + 2q−6−2q−8 + q−10 + 8q−12 + 2q−14−4q−16 + q−18 + 3q−20−5q−22−6q−24−q−26−q−28−5q−30 + 2q−34−4q−36−q−38 + 7q−40 + q−42−2q−44 + 6q−46 + 7q−48−5q−52 + 2q−54 + q−56−3q−58−3q−60−q−64−q−66 + q−72 + q−76 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | 1−q−2 + 2q−4 + 3q−6−2q−8 + 5q−10 + 5q−12−5q−14 + 8q−16 + 3q−18−8q−20 + 6q−22 + 2q−24−12q−26−3q−28−2q−30−8q−32−4q−34 + 2q−36 + 8q−38 + 3q−42 + 12q−44−5q−46−5q−48 + 9q−50−6q−52−6q−54 + 6q−56−q−58−3q−60 + 2q−62−q−66 + q−68 |
| 1,0,0 | q−1 + 2q−5 + 3q−9 + 3q−13 + q−17−q−19−2q−21−2q−23−4q−25−2q−29 + 2q−31 + 2q−35 + q−39 |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | q−2 + q−6 + 3q−8 + 2q−10 + 2q−12 + 5q−14 + 4q−16 + 2q−18 + 3q−20 + 7q−22 + q−24−2q−26 + 5q−28 + 5q−30−11q−32−10q−34−2q−36−14q−38−20q−40−8q−42 + q−44−4q−46 + 4q−48 + 18q−50 + 13q−52 + 5q−54 + 13q−56 + 9q−58−7q−60−5q−62 + 2q−64−6q−66−10q−68−q−70 + 4q−72−2q−74−3q−76 + 3q−78 + 2q−80−q−82 + q−86 |
| 1,0,0,0 | q−2 + 2q−6 + q−8 + q−10 + 3q−12 + 3q−16 + 2q−20−q−24−2q−26−3q−28−3q−30−4q−32−2q−36 + 2q−38 + q−40 + q−42 + 2q−44 + q−48 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | 1−q−2 + 4q−4−5q−6 + 8q−8−9q−10 + 13q−12−11q−14 + 12q−16−9q−18 + 6q−20−6q−24 + 12q−26−17q−28 + 20q−30−24q−32 + 22q−34−22q−36 + 16q−38−12q−40 + 5q−42−5q−46 + 9q−48−11q−50 + 12q−52−10q−54 + 10q−56−7q−58 + 5q−60−4q−62 + 2q−64−q−66 + q−68 |
| 1,0 | q2−q−2−q−4 + 3q−6 + 4q−8−q−10−5q−12 + 8q−16 + 8q−18−6q−20−9q−22 + 3q−24 + 14q−26 + 5q−28−11q−30−10q−32 + 6q−34 + 11q−36−q−38−12q−40−5q−42 + 5q−44 + 2q−46−8q−48−8q−50 + 4q−52 + 5q−54−4q−56−8q−58 + 4q−60 + 11q−62 + 3q−64−8q−66−2q−68 + 11q−70 + 9q−72−6q−74−11q−76 + q−78 + 12q−80 + 4q−82−9q−84−9q−86 + q−88 + 8q−90 + 2q−92−4q−94−4q−96 + 3q−100 + q−102−q−104−q−106 + q−110 |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | q−2−q−4 + 3q−6−2q−8 + 7q−10−4q−12 + 9q−14−6q−16 + 13q−18−8q−20 + 10q−22−7q−24 + 9q−26−3q−28 + 2q−30 + 2q−32−6q−34 + 5q−36−17q−38 + 8q−40−22q−42 + 11q−44−24q−46 + 15q−48−15q−50 + 18q−52−7q−54 + 13q−56 + 7q−60 + 5q−62−4q−64 + 4q−66−9q−68 + 9q−70−10q−72 + 6q−74−9q−76 + 8q−78−5q−80 + 4q−82−4q−84 + 3q−86−2q−88 + q−90−q−92 + q−94 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q−2−q−4 + 4q−6−5q−8 + 6q−10−3q−12−2q−14 + 12q−16−18q−18 + 25q−20−23q−22 + 11q−24 + 9q−26−30q−28 + 49q−30−48q−32 + 36q−34−7q−36−25q−38 + 51q−40−55q−42 + 41q−44−8q−46−22q−48 + 41q−50−37q−52 + 15q−54 + 17q−56−40q−58 + 46q−60−32q−62−q−64 + 35q−66−64q−68 + 68q−70−53q−72 + 15q−74 + 23q−76−62q−78 + 71q−80−64q−82 + 32q−84 + 4q−86−40q−88 + 51q−90−43q−92 + 16q−94 + 15q−96−34q−98 + 34q−100−14q−102−12q−104 + 38q−106−43q−108 + 38q−110−13q−112−13q−114 + 35q−116−42q−118 + 41q−120−24q−122 + 6q−124 + 10q−126−21q−128 + 23q−130−22q−132 + 16q−134−7q−136−q−138 + 6q−140−10q−142 + 9q−144−7q−146 + 5q−148−2q−150−q−152 + 2q−154−3q−156 + 2q−158−q−160 + q−162 |
.
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
| K = Knot["10 50"];
|
In[4]:=
| Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| −2t3 + 7t2−11t + 13−11t−1 + 7t−2−2t−3 |
In[5]:=
| Conway[K][z]
|
Out[5]=
| −2z6−5z4−z2 + 1 |
In[6]:=
| Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
|
Out[7]=
| { 53, 4 } |
In[8]:=
| Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
| q10−2q9 + 4q8−7q7 + 8q6−9q5 + 8q4−6q3 + 5q2−2q + 1 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| −z6a−4−z6a−6 + z4a−2−3z4a−4−4z4a−6 + z4a−8 + 3z2a−2−z2a−4−6z2a−6 + 3z2a−8 + 2a−2 + a−4−4a−6 + 2a−8 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| z9a−5 + z9a−7 + 2z8a−4 + 5z8a−6 + 3z8a−8 + 2z7a−3 + z7a−5 + 3z7a−7 + 4z7a−9 + z6a−2−4z6a−4−15z6a−6−7z6a−8 + 3z6a−10−6z5a−3−8z5a−5−15z5a−7−11z5a−9 + 2z5a−11−4z4a−2−z4a−4 + 18z4a−6 + 9z4a−8−5z4a−10 + z4a−12 + 3z3a−3 + 6z3a−5 + 22z3a−7 + 16z3a−9−3z3a−11 + 5z2a−2−13z2a−6−3z2a−8 + 3z2a−10−2z2a−12 + za−3−3za−5−10za−7−6za−9−2a−2 + a−4 + 4a−6 + 2a−8 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, 
):
{}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 50"];
|
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]=
| { −2t3 + 7t2−11t + 13−11t−1 + 7t−2−2t−3, q10−2q9 + 4q8−7q7 + 8q6−9q5 + 8q4−6q3 + 5q2−2q + 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]=
| {} |
[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 = 4 is the signature of 10 50. 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 | q28−2q27 + q26 + 3q25−8q24 + 5q23 + 9q22−22q21 + 11q20 + 24q19−43q18 + 14q17 + 41q16−57q15 + 9q14 + 51q13−54q12−2q11 + 50q10−39q9−12q8 + 39q7−19q6−14q5 + 22q4−5q3−8q2 + 7q−2q−1 + q−2 |
| 3 | q54−2q53 + q52 + q50−3q49 + 3q48−3q46−3q45 + 12q44 + 2q43−20q42−10q41 + 37q40 + 24q39−56q38−44q37 + 67q36 + 82q35−87q34−109q33 + 84q32 + 147q31−85q30−167q29 + 67q28 + 188q27−53q26−188q25 + 26q24 + 186q23−q22−174q21−25q20 + 153q19 + 55q18−134q17−68q16 + 96q15 + 90q14−74q13−84q12 + 34q11 + 85q10−17q9−61q8−9q7 + 51q6 + 9q5−26q4−15q3 + 17q2 + 9q−6−7q−1 + 4q−2 + 2q−3−2q−5 + q−6 |
| 4 | q88−2q87 + q86−2q84 + 6q83−6q82 + 3q81−2q80−8q79 + 21q78−11q77 + 3q76−11q75−24q74 + 54q73−2q72 + 10q71−46q70−82q69 + 95q68 + 52q67 + 81q66−90q65−243q64 + 65q63 + 137q62 + 295q61−46q60−487q59−117q58 + 138q57 + 610q56 + 167q55−674q54−396q53−13q52 + 857q51 + 460q50−697q49−600q48−246q47 + 925q46 + 679q45−591q44−645q43−442q42 + 840q41 + 759q40−425q39−562q38−574q37 + 655q36 + 743q35−219q34−402q33−659q32 + 393q31 + 646q30 + 14q29−172q28−671q27 + 94q26 + 448q25 + 189q24 + 92q23−543q22−133q21 + 174q20 + 204q19 + 279q18−298q17−184q16−44q15 + 80q14 + 286q13−77q12−93q11−106q10−35q9 + 169q8 + 10q7−3q6−60q5−56q4 + 62q3 + 9q2 + 19q−16−29q−1 + 18q−2−q−3 + 9q−4−2q−5−9q−6 + 5q−7−q−8 + 2q−9−2q−11 + q−12 |
[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. |
|
