10 65
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 65's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10_65's page at Knotilus! Visit 10 65's page at the original Knot Atlas! |
[edit] Knot presentations
| Planar diagram presentation | X1425 X3,10,4,11 X11,19,12,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 X13,1,14,20 X19,13,20,12 X9,2,10,3 |
| Gauss code | -1, 10, -2, 1, -4, 5, -6, 7, -10, 2, -3, 9, -8, 4, -7, 6, -5, 3, -9, 8 |
| Dowker-Thistlethwaite code | 4 10 14 16 2 18 20 8 6 12 |
| Conway Notation | [31,3,21] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 | 
|  [{9, 2}, {1, 7}, {4, 8}, {7, 9}, {10, 13}, {8, 12}, {13, 11}, {3, 5}, {6, 4}, {5, 10}, {2, 6}, {12, 3}, {11, 1}] |
[edit Notes on presentations of 10 65]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 65"];
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In[4]:=
| PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
| X1425 X3,10,4,11 X11,19,12,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 X13,1,14,20 X19,13,20,12 X9,2,10,3 |
In[5]:=
| GaussCode[K]
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Out[5]=
| -1, 10, -2, 1, -4, 5, -6, 7, -10, 2, -3, 9, -8, 4, -7, 6, -5, 3, -9, 8 |
In[6]:=
| DTCode[K]
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Out[6]=
| 4 10 14 16 2 18 20 8 6 12 |
(The path below may be different on your system)
In[7]:=
| AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
| ConwayNotation[K]
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Out[8]=
| [31,3,21] |
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,−1,2,−3,2,2,2,−3,−3}) |
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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|
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Out[12]=
| -Graphics- |
In[13]:=
| ap = ArcPresentation[K]
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Out[13]=
| ArcPresentation[{9, 2}, {1, 7}, {4, 8}, {7, 9}, {10, 13}, {8, 12}, {13, 11}, {3, 5}, {6, 4}, {5, 10}, {2, 6}, {12, 3}, {11, 1}] |
In[14]:=
| Draw[ap]
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|
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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 | 2t3−7t2 + 14t−17 + 14t−1−7t−2 + 2t−3 |
| Conway polynomial | 2z6 + 5z4 + 4z2 + 1 |
| 2nd Alexander ideal (db, data sources) |  |
| Determinant and Signature | { 63, 2 } |
| Jones polynomial | −q8 + 2q7−5q6 + 8q5−9q4 + 11q3−10q2 + 8q−5 + 3q−1−q−2 |
| HOMFLY-PT polynomial (db, data sources) | z6a−2 + z6a−4 + 3z4a−2 + 4z4a−4−z4a−6−z4 + 2z2a−2 + 7z2a−4−3z2a−6−2z2−a−2 + 5a−4−3a−6 |
| Kauffman polynomial (db, data sources) | z9a−3 + z9a−5 + 3z8a−2 + 6z8a−4 + 3z8a−6 + 4z7a−1 + 5z7a−3 + 4z7a−5 + 3z7a−7−4z6a−2−16z6a−4−7z6a−6 + 2z6a−8 + 3z6 + az5−9z5a−1−17z5a−3−14z5a−5−6z5a−7 + z5a−9 + z4a−2 + 24z4a−4 + 12z4a−6−4z4a−8−7z4−2az3 + 6z3a−1 + 20z3a−3 + 19z3a−5 + 4z3a−7−3z3a−9−z2a−2−17z2a−4−12z2a−6 + z2a−8 + 3z2−2za−1−6za−3−8za−5−2za−7 + 2za−9 + a−2 + 5a−4 + 3a−6 |
| The A2 invariant | −q6 + q4 + 2q−2−3q−4 + q−6 + 2q−10 + 4q−12 + 2q−16−2q−18−2q−20−q−24 |
| The G2 invariant | q32−2q30 + 4q28−7q26 + 6q24−5q22−2q20 + 14q18−23q16 + 32q14−32q12 + 19q10 + 2q8−34q6 + 62q4−74q2 + 66−35q−2−10q−4 + 61q−6−92q−8 + 96q−10−66q−12 + 10q−14 + 41q−16−75q−18 + 71q−20−34q−22−13q−24 + 60q−26−74q−28 + 46q−30 + 8q−32−78q−34 + 118q−36−116q−38 + 74q−40−75q−44 + 136q−46−141q−48 + 113q−50−48q−52−31q−54 + 93q−56−103q−58 + 85q−60−32q−62−18q−64 + 62q−66−63q−68 + 30q−70 + 15q−72−66q−74 + 88q−76−72q−78 + 17q−80 + 38q−82−82q−84 + 99q−86−84q−88 + 41q−90 + 2q−92−47q−94 + 64q−96−62q−98 + 43q−100−17q−102−3q−104 + 16q−106−23q−108 + 21q−110−15q−112 + 8q−114−q−116−3q−118 + 4q−120−4q−122 + 3q−124−q−126 + q−128 |
Further Quantum Invariants
Further quantum knot invariants for 10_65.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | −q5 + 2q3−2q + 3q−1−2q−3 + q−5 + 2q−7−q−9 + 3q−11−3q−13 + q−15−q−17 |
| 2 | q16−2q14−q12 + 6q10−5q8−6q6 + 13q4−4q2−14 + 18q−2 + 3q−4−18q−6 + 13q−8 + 9q−10−12q−12−2q−14 + 8q−16 + 2q−18−14q−20 + 6q−22 + 15q−24−17q−26−q−28 + 18q−30−13q−32−7q−34 + 12q−36−4q−38−5q−40 + 4q−42−q−46 + q−48 |
| 3 | −q33 + 2q31 + q29−3q27−3q25 + 5q23 + 8q21−9q19−14q17 + 10q15 + 24q13−10q11−38q9 + 2q7 + 55q5 + 12q3−66q−36q−1 + 73q−3 + 61q−5−64q−7−81q−9 + 49q−11 + 95q−13−28q−15−92q−17 + 5q−19 + 80q−21 + 22q−23−61q−25−37q−27 + 36q−29 + 55q−31−13q−33−71q−35−15q−37 + 77q−39 + 38q−41−81q−43−57q−45 + 71q−47 + 78q−49−55q−51−83q−53 + 30q−55 + 84q−57−10q−59−68q−61−13q−63 + 50q−65 + 20q−67−31q−69−19q−71 + 13q−73 + 15q−75−5q−77−7q−79 + 2q−81 + 4q−83−q−85−q−87 + q−91−q−93 |
| 4 | q56−2q54−q52 + 3q50 + 3q46−8q44−3q42 + 11q40 + q38 + 9q36−24q34−16q32 + 28q30 + 19q28 + 27q26−60q24−64q22 + 32q20 + 71q18 + 112q16−73q14−178q12−72q10 + 95q8 + 300q6 + 60q4−255q2−315−64q−2 + 446q−4 + 356q−6−115q−8−502q−10−383q−12 + 345q−14 + 570q−16 + 186q−18−433q−20−589q−22 + 71q−24 + 510q−26 + 385q−28−185q−30−526q−32−165q−34 + 274q−36 + 395q−38 + 49q−40−317q−42−285q−44 + 40q−46 + 322q−48 + 228q−50−102q−52−382q−54−182q−56 + 250q−58 + 402q−60 + 112q−62−449q−64−408q−66 + 113q−68 + 522q−70 + 369q−72−366q−74−557q−76−139q−78 + 439q−80 + 558q−82−95q−84−478q−86−363q−88 + 146q−90 + 501q−92 + 162q−94−190q−96−349q−98−119q−100 + 238q−102 + 198q−104 + 48q−106−159q−108−154q−110 + 31q−112 + 78q−114 + 85q−116−16q−118−63q−120−15q−122 + 33q−126 + 7q−128−12q−130−q−132−7q−134 + 6q−136 + q−138−3q−140 + 2q−142−2q−144 + q−146−q−150 + q−152 |
| 5 | −q85 + 2q83 + q81−3q79 + 3q71 + 2q69−7q67−5q65 + 7q63 + 9q61 + 5q59−6q57−22q55−23q53 + 14q51 + 56q49 + 46q47−11q45−88q43−116q41−32q39 + 133q37 + 227q35 + 127q33−122q31−353q29−341q27 + 7q25 + 464q23 + 634q21 + 284q19−435q17−972q15−779q13 + 162q11 + 1207q9 + 1436q7 + 421q5−1191q3−2079q−1306q−1 + 775q−3 + 2547q−5 + 2326q−7 + 22q−9−2599q−11−3241q−13−1110q−15 + 2199q−17 + 3837q−19 + 2214q−21−1405q−23−3926q−25−3100q−27 + 405q−29 + 3543q−31 + 3593q−33 + 548q−35−2816q−37−3597q−39−1292q−41 + 1927q−43 + 3245q−45 + 1733q−47−1090q−49−2682q−51−1863q−53 + 385q−55 + 2048q−57 + 1855q−59 + 141q−61−1532q−63−1778q−65−542q−67 + 1093q−69 + 1789q−71 + 931q−73−783q−75−1903q−77−1373q−79 + 485q−81 + 2095q−83 + 1935q−85−93q−87−2293q−89−2577q−91−448q−93 + 2332q−95 + 3215q−97 + 1187q−99−2117q−101−3711q−103−2022q−105 + 1545q−107 + 3878q−109 + 2850q−111−692q−113−3607q−115−3422q−117−365q−119 + 2908q−121 + 3623q−123 + 1317q−125−1862q−127−3303q−129−2033q−131 + 724q−133 + 2618q−135 + 2259q−137 + 258q−139−1652q−141−2071q−143−910q−145 + 739q−147 + 1557q−149 + 1111q−151−28q−153−927q−155−994q−157−363q−159 + 393q−161 + 693q−163 + 445q−165−32q−167−367q−169−368q−171−116q−173 + 140q−175 + 221q−177 + 132q−179−16q−181−105q−183−87q−185−25q−187 + 34q−189 + 48q−191 + 19q−193−9q−195−14q−197−12q−199−5q−201 + 9q−203 + 5q−205−2q−207 + q−209−3q−213 + q−215 + 2q−217−q−219 + q−223−q−225 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | −q6 + q4 + 2q−2−3q−4 + q−6 + 2q−10 + 4q−12 + 2q−16−2q−18−2q−20−q−24 |
| 1,1 | q20−4q18 + 10q16−22q14 + 44q12−74q10 + 112q8−166q6 + 226q4−282q2 + 328−366q−2 + 369q−4−324q−6 + 240q−8−110q−10−46q−12 + 240q−14−418q−16 + 580q−18−691q−20 + 752q−22−746q−24 + 678q−26−560q−28 + 392q−30−210q−32 + 32q−34 + 125q−36−254q−38 + 340q−40−370q−42 + 357q−44−326q−46 + 272q−48−210q−50 + 151q−52−106q−54 + 68q−56−42q−58 + 25q−60−12q−62 + 6q−64−2q−66 + q−68 |
| 2,0 | q18−q16−2q14 + 2q12 + 3q10−3q8−5q6 + 4q4 + 5q2−7−6q−2 + 8q−4 + 2q−6−6q−8 + 5q−10 + 11q−12 + 2q−14−3q−16 + 3q−18−2q−20−11q−22 + q−24 + 5q−26−4q−28 + q−30 + 14q−32 + 6q−34−5q−36−2q−38 + 3q−40−5q−42−11q−44−2q−46 + 2q−48−q−50−q−52 + q−54 + 2q−56 + q−58 + q−62 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | q14−2q12 + 3q8−6q6 + 3q4 + 8q2−11 + 3q−2 + 11q−4−17q−6−q−8 + 12q−10−10q−12 + 11q−16 + 4q−18 + q−20 + 2q−22 + 12q−24−3q−26−11q−28 + 11q−30−3q−32−18q−34 + 10q−36−12q−40 + 7q−42 + q−44−4q−46 + 3q−48 + q−50−q−52 + q−54 |
| 1,0,0 | −q7 + q5−q3 + 2q−q−1 + 2q−3−3q−5−q−9 + q−11 + 3q−13 + 3q−15 + 5q−17 + 2q−21−3q−23−q−25−3q−27−q−31 |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | q16−q14−q12 + q10−q8−2q6 + 3q4 + 4q2−3−2q−2 + 6q−4 + 2q−6−13q−8−2q−10 + 10q−12−6q−14−11q−16 + 8q−18 + 7q−20−8q−22 + 2q−24 + 16q−26 + 7q−28 + 2q−30 + 19q−32 + 15q−34−8q−36 + 5q−40−15q−42−21q−44−3q−46−q−48−11q−50−5q−52 + 7q−54 + 4q−56−3q−58 + 3q−60 + 4q−62 + q−68 |
| 1,0,0,0 | −q8 + q6−q4 + q2 + 1−q−2 + 2q−4−3q−6−2q−10 + q−14 + 3q−16 + 4q−18 + 4q−20 + 5q−22 + 2q−26−3q−28−2q−30−2q−32−3q−34−q−38 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | −q14 + 2q12−4q10 + 7q8−10q6 + 13q4−16q2 + 17−17q−2 + 15q−4−9q−6 + 3q−8 + 6q−10−14q−12 + 24q−14−29q−16 + 34q−18−33q−20 + 32q−22−26q−24 + 19q−26−9q−28 + q−30 + 7q−32−12q−34 + 16q−36−18q−38 + 16q−40−15q−42 + 11q−44−8q−46 + 5q−48−3q−50 + q−52−q−54 |
| 1,0 | q24−2q20−2q18 + 2q16 + 5q14−q12−8q10−4q8 + 9q6 + 12q4−4q2−16−5q−2 + 15q−4 + 14q−6−10q−8−19q−10−q−12 + 17q−14 + 7q−16−12q−18−9q−20 + 10q−22 + 12q−24−4q−26−10q−28 + 5q−30 + 13q−32 + q−34−11q−36−q−38 + 13q−40 + 7q−42−12q−44−11q−46 + 9q−48 + 16q−50−4q−52−20q−54−9q−56 + 14q−58 + 13q−60−8q−62−16q−64−3q−66 + 11q−68 + 6q−70−4q−72−6q−74 + 4q−78 + 2q−80−q−82−q−84 + q−88 |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | q18−2q16 + 2q14−4q12 + 6q10−8q8 + 9q6−10q4 + 14q2−13 + 13q−2−12q−4 + 12q−6−11q−8 + q−10−3q−12−4q−14 + 8q−16−16q−18 + 19q−20−17q−22 + 32q−24−20q−26 + 31q−28−19q−30 + 29q−32−15q−34 + 14q−36−14q−38 + 2q−40−2q−42−8q−44 + 2q−46−14q−48 + 12q−50−14q−52 + 12q−54−14q−56 + 12q−58−9q−60 + 7q−62−6q−64 + 5q−66−2q−68 + 2q−70−q−72 + q−74 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | q32−2q30 + 4q28−7q26 + 6q24−5q22−2q20 + 14q18−23q16 + 32q14−32q12 + 19q10 + 2q8−34q6 + 62q4−74q2 + 66−35q−2−10q−4 + 61q−6−92q−8 + 96q−10−66q−12 + 10q−14 + 41q−16−75q−18 + 71q−20−34q−22−13q−24 + 60q−26−74q−28 + 46q−30 + 8q−32−78q−34 + 118q−36−116q−38 + 74q−40−75q−44 + 136q−46−141q−48 + 113q−50−48q−52−31q−54 + 93q−56−103q−58 + 85q−60−32q−62−18q−64 + 62q−66−63q−68 + 30q−70 + 15q−72−66q−74 + 88q−76−72q−78 + 17q−80 + 38q−82−82q−84 + 99q−86−84q−88 + 41q−90 + 2q−92−47q−94 + 64q−96−62q−98 + 43q−100−17q−102−3q−104 + 16q−106−23q−108 + 21q−110−15q−112 + 8q−114−q−116−3q−118 + 4q−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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
| K = Knot["10 65"];
|
In[4]:=
| Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
| 2t3−7t2 + 14t−17 + 14t−1−7t−2 + 2t−3 |
In[5]:=
| Conway[K][z]
|
Out[5]=
| 2z6 + 5z4 + 4z2 + 1 |
In[6]:=
| Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
|
|
In[7]:=
| {KnotDet[K], KnotSignature[K]}
|
Out[7]=
| { 63, 2 } |
In[8]:=
| Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
| −q8 + 2q7−5q6 + 8q5−9q4 + 11q3−10q2 + 8q−5 + 3q−1−q−2 |
In[9]:=
| HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
| z6a−2 + z6a−4 + 3z4a−2 + 4z4a−4−z4a−6−z4 + 2z2a−2 + 7z2a−4−3z2a−6−2z2−a−2 + 5a−4−3a−6 |
In[10]:=
| Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
| z9a−3 + z9a−5 + 3z8a−2 + 6z8a−4 + 3z8a−6 + 4z7a−1 + 5z7a−3 + 4z7a−5 + 3z7a−7−4z6a−2−16z6a−4−7z6a−6 + 2z6a−8 + 3z6 + az5−9z5a−1−17z5a−3−14z5a−5−6z5a−7 + z5a−9 + z4a−2 + 24z4a−4 + 12z4a−6−4z4a−8−7z4−2az3 + 6z3a−1 + 20z3a−3 + 19z3a−5 + 4z3a−7−3z3a−9−z2a−2−17z2a−4−12z2a−6 + z2a−8 + 3z2−2za−1−6za−3−8za−5−2za−7 + 2za−9 + a−2 + 5a−4 + 3a−6 |
[edit] "Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {10_77, K11n71, K11n75,}
Same Jones Polynomial (up to mirroring, 
):
{}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
| AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
| K = Knot["10 65"];
|
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 + 14t−17 + 14t−1−7t−2 + 2t−3, −q8 + 2q7−5q6 + 8q5−9q4 + 11q3−10q2 + 8q−5 + 3q−1−q−2 } |
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]=
| {10_77, K11n71, K11n75,} |
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 = 2 is the signature of 10 65. 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 + q21 + 5q20−11q19 + 2q18 + 21q17−30q16−4q15 + 52q14−49q13−20q12 + 84q11−58q10−40q9 + 100q8−52q7−50q6 + 90q5−31q4−46q3 + 59q2−10q−31 + 27q−1−14q−3 + 8q−4 + q−5−3q−6 + q−7 |
| 3 | −q45 + 2q44−q43−q42−q41 + 7q40−3q39−10q38 + q37 + 27q36−5q35−42q34−11q33 + 78q32 + 25q31−105q30−66q29 + 136q28 + 119q27−159q26−179q25 + 164q24 + 252q23−166q22−307q21 + 140q20 + 371q19−127q18−399q17 + 84q16 + 429q15−59q14−418q13 + 11q12 + 405q11 + 24q10−360q9−64q8 + 308q7 + 88q6−237q5−110q4 + 178q3 + 105q2−112q−98 + 69q−1 + 75q−2−34q−3−55q−4 + 16q−5 + 35q−6−6q−7−21q−8 + 2q−9 + 11q−10−q−11−4q−12−q−13 + 3q−14−q−15 |
| 4 | q74−2q73 + q72 + q71−3q70 + 5q69−7q68 + 5q67 + 6q66−16q65 + 11q64−18q63 + 24q62 + 32q61−49q60−4q59−66q58 + 71q57 + 133q56−56q55−51q54−251q53 + 66q52 + 340q51 + 94q50−11q49−608q48−164q47 + 499q46 + 446q45 + 328q44−963q43−673q42 + 384q41 + 829q40 + 981q39−1082q38−1251q37−34q36 + 1020q35 + 1716q34−929q33−1660q32−555q31 + 979q30 + 2277q29−639q28−1812q27−987q26 + 779q25 + 2557q24−309q23−1718q22−1269q21 + 454q20 + 2525q19 + 57q18−1372q17−1390q16 + 15q15 + 2164q14 + 398q13−802q12−1265q11−424q10 + 1504q9 + 554q8−183q7−881q6−649q5 + 776q4 + 435q3 + 204q2−410q−559 + 266q−1 + 184q−2 + 264q−3−95q−4−319q−5 + 61q−6 + 17q−7 + 158q−8 + 10q−9−134q−10 + 20q−11−22q−12 + 62q−13 + 14q−14−47q−15 + 12q−16−13q−17 + 18q−18 + 6q−19−14q−20 + 4q−21−3q−22 + 4q−23 + q−24−3q−25 + q−26 |
[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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