10 111
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 111's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_111's page at Knotilus! Visit 10 111's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X6271 X10,4,11,3 X14,8,15,7 X8,14,9,13 X2,10,3,9 X18,12,19,11 X16,5,17,6 X4,17,5,18 X20,16,1,15 X12,20,13,19 |
| Gauss code | 1, -5, 2, -8, 7, -1, 3, -4, 5, -2, 6, -10, 4, -3, 9, -7, 8, -6, 10, -9 |
| Dowker-Thistlethwaite code | 6 10 16 14 2 18 8 20 4 12 |
| Conway Notation | [2.2.20.2] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 | 
|  [{4, 12}, {3, 8}, {9, 5}, {8, 11}, {12, 10}, {7, 4}, {5, 2}, {1, 3}, {6, 9}, {2, 7}, {11, 6}, {10, 1}] |
[edit Notes on presentations of 10 111]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
| K = Knot["10 111"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X6271 X10,4,11,3 X14,8,15,7 X8,14,9,13 X2,10,3,9 X18,12,19,11 X16,5,17,6 X4,17,5,18 X20,16,1,15 X12,20,13,19 |
In[5]:=
| GaussCode[K]
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Out[5]=
| 1, -5, 2, -8, 7, -1, 3, -4, 5, -2, 6, -10, 4, -3, 9, -7, 8, -6, 10, -9 |
In[6]:=
| DTCode[K]
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Out[6]=
| 6 10 16 14 2 18 8 20 4 12 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [2.2.20.2] |
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(4,{1,1,2,2,−3,2,2,−1,2,−3,2}) |
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]=
| { 4, 11, 4 } |
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[{4, 12}, {3, 8}, {9, 5}, {8, 11}, {12, 10}, {7, 4}, {5, 2}, {1, 3}, {6, 9}, {2, 7}, {11, 6}, {10, 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 | −2t3 + 9t2−17t + 21−17t−1 + 9t−2−2t−3 |
| Conway polynomial | −2z6−3z4 + z2 + 1 |
| 2nd Alexander ideal (db, data sources) | {1} |
| Determinant and Signature | { 77, 4 } |
| Jones polynomial | q10−3q9 + 6q8−10q7 + 12q6−13q5 + 12q4−9q3 + 7q2−3q + 1 |
| HOMFLY-PT polynomial (db, data sources) | −z6a−4−z6a−6 + z4a−2−2z4a−4−3z4a−6 + z4a−8 + 2z2a−2 + z2a−4−4z2a−6 + 2z2a−8 + a−2 + 2a−4−3a−6 + a−8 |
| Kauffman polynomial (db, data sources) | 2z9a−5 + 2z9a−7 + 4z8a−4 + 10z8a−6 + 6z8a−8 + 3z7a−3 + 3z7a−5 + 7z7a−7 + 7z7a−9 + z6a−2−9z6a−4−26z6a−6−11z6a−8 + 5z6a−10−8z5a−3−20z5a−5−28z5a−7−13z5a−9 + 3z5a−11−3z4a−2 + 3z4a−4 + 22z4a−6 + 10z4a−8−5z4a−10 + z4a−12 + 5z3a−3 + 19z3a−5 + 30z3a−7 + 13z3a−9−3z3a−11 + 3z2a−2−2z2a−4−10z2a−6−3z2a−8 + z2a−10−z2a−12−za−3−7za−5−10za−7−4za−9−a−2 + 2a−4 + 3a−6 + a−8 |
| The A2 invariant | 1−q−2 + q−4 + 2q−6−q−8 + 4q−10−q−12 + q−14−3q−18 + q−20−3q−22 + q−24 + q−26−q−28 + q−30 |
| The G2 invariant | q−2−2q−4 + 6q−6−10q−8 + 13q−10−11q−12 + q−14 + 20q−16−43q−18 + 67q−20−74q−22 + 48q−24 + 8q−26−84q−28 + 152q−30−169q−32 + 131q−34−35q−36−85q−38 + 181q−40−207q−42 + 155q−44−36q−46−85q−48 + 163q−50−153q−52 + 71q−54 + 49q−56−142q−58 + 171q−60−123q−62 + 10q−64 + 117q−66−214q−68 + 239q−70−182q−72 + 57q−74 + 88q−76−213q−78 + 259q−80−226q−82 + 114q−84 + 29q−86−152q−88 + 201q−90−163q−92 + 57q−94 + 65q−96−143q−98 + 139q−100−64q−102−48q−104 + 143q−106−173q−108 + 137q−110−44q−112−60q−114 + 134q−116−157q−118 + 131q−120−68q−122 + 2q−124 + 50q−126−77q−128 + 77q−130−60q−132 + 38q−134−12q−136−9q−138 + 21q−140−28q−142 + 24q−144−17q−146 + 10q−148−2q−150−3q−152 + 5q−154−6q−156 + 4q−158−2q−160 + q−162 |
Further Quantum Invariants
Further quantum knot invariants for 10_111.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | q−2q−1 + 4q−3−2q−5 + 3q−7−q−9−q−11 + 2q−13−4q−15 + 3q−17−2q−19 + q−21 |
| 2 | q6−2q4−q2 + 9−5q−2−13q−4 + 20q−6 + 5q−8−27q−10 + 15q−12 + 20q−14−27q−16 + 23q−20−13q−22−12q−24 + 14q−26 + 7q−28−19q−30−4q−32 + 27q−34−14q−36−20q−38 + 29q−40−2q−42−20q−44 + 14q−46 + 3q−48−8q−50 + 4q−52−2q−56 + q−58 |
| 3 | q15−2q13−q11 + 4q9 + 6q7−8q5−19q3 + 10q + 41q−1 + 5q−3−63q−5−44q−7 + 77q−9 + 92q−11−52q−13−143q−15 + 3q−17 + 172q−19 + 66q−21−166q−23−129q−25 + 129q−27 + 177q−29−79q−31−197q−33 + 29q−35 + 190q−37 + 20q−39−176q−41−54q−43 + 143q−45 + 87q−47−112q−49−116q−51 + 62q−53 + 146q−55−3q−57−165q−59−65q−61 + 166q−63 + 132q−65−132q−67−182q−69 + 82q−71 + 196q−73−25q−75−170q−77−27q−79 + 125q−81 + 46q−83−71q−85−43q−87 + 31q−89 + 27q−91−11q−93−13q−95 + 5q−97 + 3q−99−q−101 + q−105−2q−109 + q−111 |
| 4 | q28−2q26−q24 + 4q22 + q20 + 3q18−14q16−13q14 + 18q12 + 28q10 + 39q8−48q6−105q4−36q2 + 77 + 235q−2 + 81q−4−207q−6−342q−8−196q−10 + 385q−12 + 565q−14 + 197q−16−481q−18−899q−20−186q−22 + 729q−24 + 1079q−26 + 279q−28−1115q−30−1227q−32−137q−34 + 1339q−36 + 1440q−38−238q−40−1562q−42−1334q−44 + 558q−46 + 1841q−48 + 888q−50−940q−52−1780q−54−397q−56 + 1376q−58 + 1351q−60−187q−62−1488q−64−820q−66 + 761q−68 + 1266q−70 + 225q−72−1053q−74−933q−76 + 282q−78 + 1145q−80 + 592q−82−625q−84−1151q−86−392q−88 + 964q−90 + 1206q−92 + 173q−94−1266q−96−1391q−98 + 251q−100 + 1594q−102 + 1336q−104−641q−106−1978q−108−916q−110 + 1025q−112 + 1946q−114 + 507q−116−1405q−118−1474q−120−104q−122 + 1345q−124 + 1034q−126−301q−128−949q−130−607q−132 + 372q−134 + 637q−136 + 192q−138−230q−140−367q−142−30q−144 + 166q−146 + 118q−148 + 17q−150−101q−152−31q−154 + 17q−156 + 19q−158 + 22q−160−20q−162−5q−164 + q−166−q−168 + 7q−170−3q−172 + q−174−2q−178 + q−180 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | 1−q−2 + q−4 + 2q−6−q−8 + 4q−10−q−12 + q−14−3q−18 + q−20−3q−22 + q−24 + q−26−q−28 + q−30 |
| 1,1 | q4−4q2 + 14−36q−2 + 80q−4−146q−6 + 254q−8−392q−10 + 548q−12−682q−14 + 786q−16−808q−18 + 720q−20−514q−22 + 216q−24 + 150q−26−543q−28 + 906q−30−1206q−32 + 1396q−34−1471q−36 + 1408q−38−1222q−40 + 940q−42−589q−44 + 216q−46 + 126q−48−396q−50 + 574q−52−656q−54 + 650q−56−578q−58 + 486q−60−388q−62 + 292q−64−216q−66 + 161q−68−118q−70 + 82q−72−54q−74 + 34q−76−20q−78 + 10q−80−4q−82 + q−84 |
| 2,0 | q4−q2−2 + 3q−2 + 5q−4−q−6−7q−8 + 2q−10 + 13q−12−3q−14−10q−16 + 6q−18 + 11q−20−5q−22−8q−24 + 7q−26 + 3q−28−7q−30 + q−32 + 5q−34−7q−36−4q−38 + 9q−40−7q−42−10q−44 + 6q−46 + 11q−48−6q−50−9q−52 + 11q−54 + 6q−56−6q−58−5q−60 + 5q−62 + 2q−64−2q−66−q−68−q−74 + q−76 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | 1−2q−2 + 2q−4 + 4q−6−8q−8 + 7q−10 + 7q−12−15q−14 + 17q−16 + 8q−18−17q−20 + 16q−22 + 7q−24−20q−26 + q−28 + 3q−30−11q−32−6q−34 + 2q−36 + 11q−38−8q−40−3q−42 + 23q−44−13q−46−9q−48 + 22q−50−11q−52−10q−54 + 13q−56−3q−58−6q−60 + 5q−62−2q−66 + q−68 |
| 1,0,0 | q−1−q−3 + 2q−5−q−7 + 3q−9−q−11 + 4q−13 + 2q−17−q−21−q−23−4q−25 + q−27−3q−29 + 2q−31−q−33 + 2q−35−q−37 + q−39 |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | q−2−q−4 + 4q−8−q−10−3q−12 + 6q−14 + 4q−16−6q−18 + 2q−20 + 16q−22 + 2q−24−7q−26 + 15q−28 + 19q−30−16q−32−12q−34 + 13q−36−11q−38−31q−40−3q−42 + 7q−44−16q−46−5q−48 + 22q−50 + 6q−52−10q−54 + 16q−56 + 17q−58−13q−60−6q−62 + 15q−64−2q−66−16q−68 + 9q−72−4q−74−7q−76 + 4q−78 + 4q−80−2q−82−q−84 + q−86 |
| 1,0,0,0 | q−2−q−4 + 2q−6 + 3q−12−q−14 + 4q−16 + 3q−20 + q−22−q−26−2q−28−2q−30−4q−32 + q−34−3q−36 + 2q−38 + 2q−44−q−46 + q−48 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | 1−2q−2 + 6q−4−10q−6 + 16q−8−21q−10 + 27q−12−27q−14 + 27q−16−22q−18 + 15q−20−2q−22−11q−24 + 26q−26−37q−28 + 47q−30−53q−32 + 52q−34−48q−36 + 37q−38−26q−40 + 11q−42 + q−44−13q−46 + 21q−48−26q−50 + 27q−52−24q−54 + 21q−56−15q−58 + 10q−60−7q−62 + 4q−64−2q−66 + q−68 |
| 1,0 | q2−2q−2−2q−4 + 4q−6 + 7q−8−2q−10−12q−12−4q−14 + 16q−16 + 16q−18−13q−20−23q−22 + 4q−24 + 31q−26 + 13q−28−24q−30−22q−32 + 15q−34 + 27q−36−q−38−25q−40−8q−42 + 16q−44 + 9q−46−16q−48−15q−50 + 10q−52 + 14q−54−9q−56−20q−58 + 5q−60 + 23q−62 + 3q−64−23q−66−9q−68 + 23q−70 + 20q−72−15q−74−26q−76 + 4q−78 + 28q−80 + 9q−82−19q−84−18q−86 + 5q−88 + 17q−90 + 4q−92−9q−94−8q−96 + q−98 + 6q−100 + 2q−102−2q−104−2q−106 + q−110 |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | q−2−2q−4 + 4q−6−5q−8 + 10q−10−12q−12 + 16q−14−18q−16 + 24q−18−21q−20 + 23q−22−17q−24 + 22q−26−8q−28 + 7q−30 + 5q−32−9q−34 + 15q−36−31q−38 + 26q−40−41q−42 + 34q−44−47q−46 + 37q−48−36q−50 + 36q−52−24q−54 + 20q−56−8q−58 + 8q−60 + 7q−62−11q−64 + 13q−66−19q−68 + 23q−70−21q−72 + 16q−74−19q−76 + 17q−78−11q−80 + 8q−82−8q−84 + 6q−86−3q−88 + 2q−90−2q−92 + q−94 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q−2−2q−4 + 6q−6−10q−8 + 13q−10−11q−12 + q−14 + 20q−16−43q−18 + 67q−20−74q−22 + 48q−24 + 8q−26−84q−28 + 152q−30−169q−32 + 131q−34−35q−36−85q−38 + 181q−40−207q−42 + 155q−44−36q−46−85q−48 + 163q−50−153q−52 + 71q−54 + 49q−56−142q−58 + 171q−60−123q−62 + 10q−64 + 117q−66−214q−68 + 239q−70−182q−72 + 57q−74 + 88q−76−213q−78 + 259q−80−226q−82 + 114q−84 + 29q−86−152q−88 + 201q−90−163q−92 + 57q−94 + 65q−96−143q−98 + 139q−100−64q−102−48q−104 + 143q−106−173q−108 + 137q−110−44q−112−60q−114 + 134q−116−157q−118 + 131q−120−68q−122 + 2q−124 + 50q−126−77q−128 + 77q−130−60q−132 + 38q−134−12q−136−9q−138 + 21q−140−28q−142 + 24q−144−17q−146 + 10q−148−2q−150−3q−152 + 5q−154−6q−156 + 4q−158−2q−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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
| K = Knot["10 111"];
|
In[4]:=
| Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| −2t3 + 9t2−17t + 21−17t−1 + 9t−2−2t−3 |
In[5]:=
| Conway[K][z]
|
Out[5]=
| −2z6−3z4 + z2 + 1 |
In[6]:=
| Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
| {1} |
In[7]:=
| {KnotDet[K], KnotSignature[K]}
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Out[7]=
| { 77, 4 } |
In[8]:=
| Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
| q10−3q9 + 6q8−10q7 + 12q6−13q5 + 12q4−9q3 + 7q2−3q + 1 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| −z6a−4−z6a−6 + z4a−2−2z4a−4−3z4a−6 + z4a−8 + 2z2a−2 + z2a−4−4z2a−6 + 2z2a−8 + a−2 + 2a−4−3a−6 + a−8 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| 2z9a−5 + 2z9a−7 + 4z8a−4 + 10z8a−6 + 6z8a−8 + 3z7a−3 + 3z7a−5 + 7z7a−7 + 7z7a−9 + z6a−2−9z6a−4−26z6a−6−11z6a−8 + 5z6a−10−8z5a−3−20z5a−5−28z5a−7−13z5a−9 + 3z5a−11−3z4a−2 + 3z4a−4 + 22z4a−6 + 10z4a−8−5z4a−10 + z4a−12 + 5z3a−3 + 19z3a−5 + 30z3a−7 + 13z3a−9−3z3a−11 + 3z2a−2−2z2a−4−10z2a−6−3z2a−8 + z2a−10−z2a−12−za−3−7za−5−10za−7−4za−9−a−2 + 2a−4 + 3a−6 + a−8 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, 
):
{}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 111"];
|
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 + 9t2−17t + 21−17t−1 + 9t−2−2t−3, q10−3q9 + 6q8−10q7 + 12q6−13q5 + 12q4−9q3 + 7q2−3q + 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 10 111. 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 | q28−3q27 + 2q26 + 5q25−15q24 + 13q23 + 16q22−49q21 + 31q20 + 47q19−98q18 + 37q17 + 88q16−129q15 + 22q14 + 114q13−122q12−4q11 + 113q10−86q9−27q8 + 86q7−39q6−32q5 + 44q4−7q3−17q2 + 11q + 1−3q−1 + q−2 |
| 3 | q54−3q53 + 2q52 + q51−4q49 + 6q48 + 3q47−18q46−2q45 + 44q44 + 7q43−92q42−30q41 + 161q40 + 86q39−244q38−173q37 + 306q36 + 307q35−358q34−437q33 + 356q32 + 571q31−324q30−668q29 + 256q28 + 733q27−175q26−752q25 + 78q24 + 737q23 + 24q22−696q21−119q20 + 615q19 + 220q18−526q17−280q16 + 389q15 + 338q14−270q13−328q12 + 131q11 + 301q10−38q9−222q8−38q7 + 155q6 + 53q5−78q4−53q3 + 34q2 + 34q−10−17q−1 + 3q−2 + 5q−3 + q−4−3q−5 + q−6 |
| 4 | q88−3q87 + 2q86 + q85−4q84 + 11q83−11q82 + 4q81−5q80−19q79 + 53q78−14q77 + 2q76−53q75−89q74 + 171q73 + 87q72 + 50q71−249q70−426q69 + 308q68 + 509q67 + 495q66−514q65−1405q64−34q63 + 1157q62 + 1830q61−203q60−2854q59−1404q58 + 1226q57 + 3742q56 + 1236q55−3775q54−3345q53 + 164q52 + 5079q51 + 3213q50−3517q49−4688q48−1478q47 + 5204q46 + 4652q45−2484q44−4930q43−2834q42 + 4445q41 + 5178q40−1267q39−4377q38−3697q37 + 3230q36 + 5058q35 + 11q34−3336q33−4202q32 + 1649q31 + 4390q30 + 1312q29−1798q28−4177q27−124q26 + 3007q25 + 2152q24 + 30q23−3224q22−1407q21 + 1115q20 + 1924q19 + 1354q18−1546q17−1508q16−361q15 + 834q14 + 1466q13−152q12−708q11−711q10−81q9 + 753q8 + 266q7−30q6−343q5−261q4 + 172q3 + 120q2 + 105q−55−107q−1 + 14q−2 + 7q−3 + 36q−4 + 2q−5−20q−6 + 3q−7−3q−8 + 5q−9 + q−10−3q−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. |
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