10 119

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10_118

10_120

Contents

Image:10 119.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 10 119's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 10_119's page at Knotilus!

Visit 10 119's page at the original Knot Atlas!

[edit 10 119 Quick Notes]
[edit 10 119 Further Notes and Views]


[edit] Knot presentations

Planar diagram presentation X1627 X7,18,8,19 X3948 X17,3,18,2 X5,15,6,14 X9,17,10,16 X15,11,16,10 X11,5,12,4 X13,20,14,1 X19,12,20,13
Gauss code -1, 4, -3, 8, -5, 1, -2, 3, -6, 7, -8, 10, -9, 5, -7, 6, -4, 2, -10, 9
Dowker-Thistlethwaite code 6 8 14 18 16 4 20 10 2 12
Conway Notation [8*2:.20]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart2.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart0.gif

Length is 11, width is 4,

Braid index is 4

Image:10 119_ML.gif Image:10 119_AP.gif
[{12, 3}, {1, 5}, {6, 4}, {5, 2}, {3, 7}, {11, 6}, {8, 12}, {7, 9}, {2, 8}, {4, 10}, {9, 11}, {10, 1}]

[edit Notes on presentations of 10 119]


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.

Read more at http://katlas.org/wiki/KnotTheory.

In[3]:= K = Knot["10 119"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X1627 X7,18,8,19 X3948 X17,3,18,2 X5,15,6,14 X9,17,10,16 X15,11,16,10 X11,5,12,4 X13,20,14,1 X19,12,20,13
In[5]:= GaussCode[K]
Out[5]= -1, 4, -3, 8, -5, 1, -2, 3, -6, 7, -8, 10, -9, 5, -7, 6, -4, 2, -10, 9
In[6]:= DTCode[K]
Out[6]= 6 8 14 18 16 4 20 10 2 12

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [8*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(4,{−1,−1,2,−1,−3,2,−1,2,3,3,2})
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]]
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart2.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart0.gif
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."
Image:10 119_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{12, 3}, {1, 5}, {6, 4}, {5, 2}, {3, 7}, {11, 6}, {8, 12}, {7, 9}, {2, 8}, {4, 10}, {9, 11}, {10, 1}]
In[14]:= Draw[ap]
Image:10 119_AP.gif
Out[14]= -Graphics-

[edit] Three dimensional invariants

Symmetry type Chiral
Unknotting number 1
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-5][-7]
Hyperbolic Volume 15.9387
A-Polynomial See Data:10 119/A-polynomial

[edit Notes for 10 119's three dimensional invariants]

[edit] Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 0

[edit Notes for 10 119's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial −2t3 + 10t2−23t + 31−23t−1 + 10t−2−2t−3
Conway polynomial −2z6−2z4−z2 + 1
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 101, 0 }
Jones polynomial q6−4q5 + 8q4−12q3 + 16q2−17q + 16−13q−1 + 9q−2−4q−3 + q−4
HOMFLY-PT polynomial (db, data sources) −z6a−2−z6 + a2z4−2z4a−2 + z4a−4−2z4 + a2z2−z2a−2 + z2a−4−2z2 + a2 + a−2−1
Kauffman polynomial (db, data sources) 3z9a−1 + 3z9a−3 + 15z8a−2 + 6z8a−4 + 9z8 + 12az7 + 13z7a−1 + 5z7a−3 + 4z7a−5 + 9a2z6−31z6a−2−14z6a−4 + z6a−6−7z6 + 4a3z5−17az5−37z5a−1−26z5a−3−10z5a−5 + a4z4−9a2z4 + 13z4a−2 + 8z4a−4−2z4a−6−7z4−a3z3 + 9az3 + 22z3a−1 + 19z3a−3 + 7z3a−5 + 4a2z2 + z2a−2 + z2a−6 + 6z2−2az−4za−1−3za−3−za−5−a2−a−2−1
The A2 invariant q12−2q10 + 2q8 + 2q6−3q4 + 3q2−3 + q−2 + q−4−q−6 + 4q−8−3q−10 + q−12 + q−14−2q−16 + q−18
The G2 invariant q66−3q64 + 6q62−10q60 + 11q58−10q56 + 4q54 + 14q52−35q50 + 60q48−78q46 + 71q44−44q42−17q40 + 105q38−184q36 + 238q34−223q32 + 127q30 + 33q28−222q26 + 371q24−410q22 + 305q20−82q18−176q16 + 370q14−400q12 + 264q10−15q8−242q6 + 363q4−299q2 + 59 + 250q−2−475q−4 + 516q−6−332q−8−q−10 + 350q−12−598q−14 + 642q−16−473q−18 + 155q−20 + 204q−22−467q−24 + 561q−26−441q−28 + 178q−30 + 115q−32−337q−34 + 382q−36−246q−38−7q−40 + 274q−42−413q−44 + 359q−46−130q−48−174q−50 + 415q−52−496q−54 + 387q−56−150q−58−116q−60 + 311q−62−370q−64 + 302q−66−149q−68−7q−70 + 108q−72−148q−74 + 125q−76−73q−78 + 27q−80 + 8q−82−22q−84 + 21q−86−16q−88 + 8q−90−3q−92 + q−94
Further Quantum Invariants
Further quantum knot invariants for 10_119.

A1 Invariants.

Weight Invariant
1 q9−3q7 + 5q5−4q3 + 3q−q−1−q−3 + 4q−5−4q−7 + 4q−9−3q−11 + q−13
2 q26−3q24 + 2q22 + 8q20−18q18 + 4q16 + 31q14−38q12−9q10 + 54q8−32q6−29q4 + 47q2−33q−2 + 10q−4 + 28q−6−19q−8−29q−10 + 41q−12 + 8q−14−52q−16 + 31q−18 + 31q−20−48q−22 + 4q−24 + 32q−26−20q−28−9q−30 + 13q−32−q−34−3q−36 + q−38
3 q51−3q49 + 2q47 + 5q45−6q43−11q41 + 12q39 + 32q37−32q35−68q33 + 55q31 + 132q29−55q27−237q25 + 26q23 + 343q21 + 57q19−417q17−186q15 + 425q13 + 319q11−350q9−411q7 + 215q5 + 441q3−53q−408q−1−100q−3 + 332q−5 + 225q−7−236q−9−317q−11 + 136q−13 + 386q−15−30q−17−435q−19−77q−21 + 448q−23 + 195q−25−420q−27−316q−29 + 346q−31 + 404q−33−214q−35−444q−37 + 63q−39 + 411q−41 + 73q−43−313q−45−158q−47 + 185q−49 + 175q−51−74q−53−135q−55 + 2q−57 + 78q−59 + 24q−61−34q−63−17q−65 + 8q−67 + 8q−69−q−71−3q−73 + q−75

A2 Invariants.

Weight Invariant
1,0 q12−2q10 + 2q8 + 2q6−3q4 + 3q2−3 + q−2 + q−4−q−6 + 4q−8−3q−10 + q−12 + q−14−2q−16 + q−18
1,1 q36−6q34 + 18q32−38q30 + 77q28−150q26 + 258q24−404q22 + 617q20−892q18 + 1198q16−1522q14 + 1824q12−2026q10 + 2036q8−1802q6 + 1301q4−514q2−480 + 1584q−2−2643q−4 + 3530q−6−4132q−8 + 4358q−10−4205q−12 + 3680q−14−2842q−16 + 1796q−18−674q−20−386q−22 + 1298q−24−1946q−26 + 2274q−28−2298q−30 + 2086q−32−1722q−34 + 1284q−36−874q−38 + 540q−40−296q−42 + 145q−44−62q−46 + 22q−48−6q−50 + q−52
2,0 q32−2q30 + 6q26−3q24−10q22 + 5q20 + 17q18−6q16−23q14 + 8q12 + 24q10−15q8−19q6 + 19q4 + 13q2−10−6q−2 + 13q−4−4q−6−10q−8 + 11q−10−2q−12−16q−14 + 9q−16 + 20q−18−14q−20−14q−22 + 16q−24 + 15q−26−15q−28−16q−30 + 15q−32 + 9q−34−10q−36−7q−38 + 4q−40 + 6q−42−2q−44−2q−46 + q−48

A3 Invariants.

Weight Invariant
0,1,0 q28−3q26 + 10q22−11q20−7q18 + 27q16−18q14−17q12 + 41q10−19q8−23q6 + 38q4−11q2−18 + 16q−2 + 5q−4−6q−6−13q−8 + 16q−10 + 12q−12−33q−14 + 15q−16 + 25q−18−38q−20 + 12q−22 + 23q−24−30q−26 + 10q−28 + 11q−30−14q−32 + 5q−34 + 2q−36−3q−38 + q−40
1,0,0 q15−2q13 + 3q11−q9 + 3q7−3q5 + 3q3−3q + 2q−7−q−9 + 4q−11−3q−13 + 2q−15−2q−17 + 2q−19−2q−21 + q−23

A4 Invariants.

Weight Invariant
0,1,0,0 q34−2q32−2q30 + 7q28 + q26−11q24 + q22 + 17q20−2q18−22q16 + 10q14 + 26q12−20q10−25q8 + 30q6 + 13q4−31q2 + 4 + 31q−2−12q−4−23q−6 + 24q−8 + 9q−10−36q−12 + 6q−14 + 35q−16−23q−18−24q−20 + 34q−22 + 13q−24−30q−26−3q−28 + 26q−30−3q−32−20q−34 + 8q−36 + 12q−38−9q−40−4q−42 + 6q−44−q−46−2q−48 + q−50
1,0,0,0 q18−2q16 + 3q14 + 3q8−3q6 + 3q4−3q2−q−2 + q−8 + 2q−10−q−12 + 4q−14−3q−16 + 2q−18−q−20−q−22 + 2q−24−2q−26 + q−28

B2 Invariants.

Weight Invariant
0,1 q28−3q26 + 6q24−12q22 + 21q20−29q18 + 39q16−46q14 + 49q12−45q10 + 35q8−19q6−2q4 + 27q2−52 + 72q−2−87q−4 + 94q−6−91q−8 + 80q−10−60q−12 + 37q−14−11q−16−11q−18 + 30q−20−42q−22 + 49q−24−48q−26 + 42q−28−35q−30 + 24q−32−15q−34 + 8q−36−3q−38 + q−40
1,0 q46−3q42−3q40 + 3q38 + 11q36 + 4q34−16q32−18q30 + 8q28 + 33q26 + 11q24−35q22−33q20 + 21q18 + 49q16 + 3q14−49q12−24q10 + 37q8 + 37q6−22q4−40q2 + 8 + 39q−2 + 4q−4−35q−6−11q−8 + 30q−10 + 17q−12−26q−14−23q−16 + 24q−18 + 32q−20−17q−22−44q−24 + 3q−26 + 50q−28 + 20q−30−43q−32−41q−34 + 24q−36 + 50q−38−42q−42−20q−44 + 25q−46 + 26q−48−8q−50−19q−52−3q−54 + 10q−56 + 5q−58−3q−60−3q−62 + q−66

D4 Invariants.

Weight Invariant
1,0,0,0 q38−3q36 + 3q34−4q32 + 11q30−16q28 + 16q26−21q24 + 33q22−35q20 + 33q18−37q16 + 41q14−30q12 + 22q10−18q8 + 5q6 + 15q4−25q2 + 35−52q−2 + 64q−4−66q−6 + 70q−8−75q−10 + 69q−12−58q−14 + 52q−16−42q−18 + 25q−20−8q−22−q−24 + 12q−26−25q−28 + 35q−30−36q−32 + 38q−34−39q−36 + 36q−38−30q−40 + 25q−42−20q−44 + 13q−46−8q−48 + 5q−50−3q−52 + q−54

G2 Invariants.

Weight Invariant
1,0 q66−3q64 + 6q62−10q60 + 11q58−10q56 + 4q54 + 14q52−35q50 + 60q48−78q46 + 71q44−44q42−17q40 + 105q38−184q36 + 238q34−223q32 + 127q30 + 33q28−222q26 + 371q24−410q22 + 305q20−82q18−176q16 + 370q14−400q12 + 264q10−15q8−242q6 + 363q4−299q2 + 59 + 250q−2−475q−4 + 516q−6−332q−8−q−10 + 350q−12−598q−14 + 642q−16−473q−18 + 155q−20 + 204q−22−467q−24 + 561q−26−441q−28 + 178q−30 + 115q−32−337q−34 + 382q−36−246q−38−7q−40 + 274q−42−413q−44 + 359q−46−130q−48−174q−50 + 415q−52−496q−54 + 387q−56−150q−58−116q−60 + 311q−62−370q−64 + 302q−66−149q−68−7q−70 + 108q−72−148q−74 + 125q−76−73q−78 + 27q−80 + 8q−82−22q−84 + 21q−86−16q−88 + 8q−90−3q−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.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["10 119"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= −2t3 + 10t2−23t + 31−23t−1 + 10t−2−2t−3
In[5]:= Conway[K][z]
Out[5]= −2z6−2z4−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]= { 101, 0 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= q6−4q5 + 8q4−12q3 + 16q2−17q + 16−13q−1 + 9q−2−4q−3 + q−4
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= −z6a−2−z6 + a2z4−2z4a−2 + z4a−4−2z4 + a2z2−z2a−2 + z2a−4−2z2 + a2 + a−2−1
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= 3z9a−1 + 3z9a−3 + 15z8a−2 + 6z8a−4 + 9z8 + 12az7 + 13z7a−1 + 5z7a−3 + 4z7a−5 + 9a2z6−31z6a−2−14z6a−4 + z6a−6−7z6 + 4a3z5−17az5−37z5a−1−26z5a−3−10z5a−5 + a4z4−9a2z4 + 13z4a−2 + 8z4a−4−2z4a−6−7z4−a3z3 + 9az3 + 22z3a−1 + 19z3a−3 + 7z3a−5 + 4a2z2 + z2a−2 + z2a−6 + 6z2−2az−4za−1−3za−3−za−5−a2−a−2−1

[edit] "Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a84,}

Same Jones Polynomial (up to mirroring, q\leftrightarrow q^{-1}): {}

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.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["10 119"];
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 + 10t2−23t + 31−23t−1 + 10t−2−2t−3, q6−4q5 + 8q4−12q3 + 16q2−17q + 16−13q−1 + 9q−2−4q−3 + q−4 }
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]= {K11a84,}
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] Vassiliev invariants

V2 and V3: (-1, 0)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9
−4 0 8 \frac{82}{3} \frac{62}{3} 0 32 0 32 -\frac{32}{3} 0 -\frac{328}{3} -\frac{248}{3} -\frac{1951}{30} \frac{1022}{15} -\frac{9902}{45} \frac{1855}{18} -\frac{1471}{30}

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

[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 10 119. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -4-3-2-10123456χ
13          11
11         3 -3
9        51 4
7       73  -4
5      95   4
3     87    -1
1    89     -1
-1   69      3
-3  37       -4
-5 16        5
-7 3         -3
-91          1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i = −1 i = 1
r = −4 {\mathbb Z}
r = −3 {\mathbb Z}^{3}\oplus{\mathbb Z}_2 {\mathbb Z}
r = −2 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r = −1 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r = 0 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{8}
r = 1 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{8}
r = 2 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{9}
r = 3 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{7}
r = 4 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r = 5 {\mathbb Z}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r = 6 {\mathbb Z}_2 {\mathbb Z}

[edit] The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the n + 1-dimensional representation of sl(2))

 n  Jn
2 q18−4q17 + 2q16 + 15q15−26q14−9q13 + 67q12−54q11−61q10 + 146q9−54q8−144q7 + 206q6−21q5−214q4 + 216q3 + 26q2−232q + 173 + 59q−1−185q−2 + 97q−3 + 56q−4−99q−5 + 34q−6 + 27q−7−30q−8 + 7q−9 + 5q−10−4q−11 + q−12
3 q36−4q35 + 2q34 + 9q33 + q32−29q31−15q30 + 67q29 + 55q28−105q27−152q26 + 128q25 + 304q24−95q23−495q22−27q21 + 690q20 + 243q19−843q18−534q17 + 920q16 + 861q15−901q14−1196q13 + 816q12 + 1476q11−648q10−1721q9 + 458q8 + 1881q7−232q6−1971q5 + 5q4 + 1962q3 + 229q2−1864q−427 + 1654q−1 + 584q−2−1370q−3−653q−4 + 1028q−5 + 645q−6−701q−7−547q−8 + 417q−9 + 414q−10−227q−11−261q−12 + 100q−13 + 151q−14−45q−15−74q−16 + 23q−17 + 28q−18−9q−19−10q−20 + 3q−21 + 5q−22−4q−23 + q−24
4 q60−4q59 + 2q58 + 9q57−5q56−2q55−35q54 + 9q53 + 78q52 + 24q51−2q50−234q49−123q48 + 256q47 + 344q46 + 343q45−653q44−912q43−60q42 + 923q41 + 1908q40−284q39−2244q38−2063q37 + 229q36 + 4410q35 + 2383q34−2044q33−5254q32−3503q31 + 5323q30 + 6610q29 + 1610q28−6835q27−9280q26 + 2669q25 + 9461q24 + 7637q23−4976q22−14134q21−2500q20 + 9273q19 + 13279q18−726q17−16431q16−7818q15 + 6885q14 + 17045q13 + 3954q12−16512q11−12057q10 + 3581q9 + 18858q8 + 8212q7−14791q6−14952q5−359q4 + 18417q3 + 11734q2−10923q−15659−4667q−1 + 14854q−2 + 13309q−3−5243q−4−12982q−5−7653q−6 + 8713q−7 + 11442q−8−153q−9−7596q−10−7376q−11 + 2925q−12 + 6895q−13 + 1895q−14−2602q−15−4508q−16 + 81q−17 + 2698q−18 + 1345q−19−242q−20−1752q−21−309q−22 + 666q−23 + 403q−24 + 151q−25−454q−26−84q−27 + 124q−28 + 38q−29 + 63q−30−91q−31−2q−32 + 27q−33−8q−34 + 11q−35−14q−36 + 3q−37 + 5q−38−4q−39 + q−40
5 q90−4q89 + 2q88 + 9q87−5q86−8q85−8q84−11q83 + 20q82 + 71q81 + 29q80−74q79−149q78−157q77 + 43q76 + 386q75 + 535q74 + 142q73−629q72−1233q71−964q70 + 508q69 + 2323q68 + 2741q67 + 615q66−3068q65−5523q64−3818q63 + 2301q62 + 8706q61 + 9376q60 + 1607q59−10271q58−16735q57−10010q56 + 7863q55 + 23717q54 + 22560q53 + 908q52−26863q51−37290q50−16878q49 + 22875q48 + 50391q47 + 38553q46−9576q45−57548q44−62501q43−12860q42 + 55504q41 + 84185q40 + 41841q39−43024q38−99477q37−73282q36 + 21200q35 + 105906q34 + 103113q33 + 6837q32−103332q31−127723q30−37512q29 + 92962q28 + 146068q27 + 67383q26−77858q25−157705q24−94208q23 + 60130q22 + 164281q21 + 117290q20−42344q19−166996q18−136672q17 + 24919q16 + 167338q15 + 153331q14−8048q13−165525q12−167906q11−9396q10 + 161160q9 + 180507q8 + 28179q7−152563q6−190371q5−48880q4 + 138440q3 + 195494q2 + 70496q−117398−193539q−1−91167q−2 + 90096q−3 + 182525q−4 + 107326q−5−58453q−6−161747q−7−115969q−8 + 26501q−9 + 132782q−10 + 114703q−11 + 1431q−12−99257q−13−103670q−14−21353q−15 + 65902q−16 + 85046q−17 + 31853q−18−37406q−19−63145q−20−33162q−21 + 16513q−22 + 41826q−23 + 28465q−24−3794q−25−24745q−26−20758q−27−2018q−28 + 12681q−29 + 13217q−30 + 3546q−31−5625q−32−7396q−33−2904q−34 + 2103q−35 + 3599q−36 + 1790q−37−611q−38−1566q−39−928q−40 + 176q−41 + 615q−42 + 361q−43−45q−44−198q−45−133q−46−q−47 + 96q−48 + 34q−49−33q−50−9q−51 + 2q−52−9q−53 + 12q−54 + 7q−55−14q−56 + 3q−57 + 5q−58−4q−59 + q−60
6 q126−4q125 + 2q124 + 9q123−5q122−8q121−14q120 + 16q119 + 13q117 + 76q116−19q115−87q114−173q113−37q112 + 32q111 + 212q110 + 597q109 + 324q108−193q107−1077q106−1170q105−1074q104 + 156q103 + 2687q102 + 3644q101 + 2879q100−1066q99−4766q98−8642q97−7628q96 + 740q95 + 10641q94 + 18227q93 + 14755q92 + 3147q91−19152q90−35574q89−31743q88−7345q87 + 31458q86 + 59060q85 + 63137q84 + 18940q83−48250q82−100827q81−104108q80−39317q79 + 63176q78 + 162419q77 + 167622q76 + 70659q75−92693q74−232947q73−253500q72−121546q71 + 132952q70 + 331550q69 + 362644q68 + 165312q67−169952q66−455762q65−502014q64−207811q63 + 237928q62 + 607679q61 + 632205q60 + 258986q59−338753q58−797916q57−763179q56−261150q55 + 483253q54 + 980938q53 + 900348q52 + 205544q51−692790q50−1177502q49−962377q48−71166q47 + 920165q46 + 1389200q45 + 936713q44−174355q43−1196663q42−1510284q41−793359q40 + 480296q39 + 1513405q38 + 1523101q37 + 489665q36−882073q35−1734843q34−1385111q33−80578q32 + 1351700q31 + 1832666q30 + 1041271q29−468324q28−1721154q27−1748009q26−549293q25 + 1105672q24 + 1949534q23 + 1414470q22−119797q21−1634951q20−1964344q19−894103q18 + 889871q17 + 2005998q16 + 1695002q15 + 170021q14−1543644q13−2140097q12−1212056q11 + 657080q10 + 2026626q9 + 1970649q8 + 515939q7−1359164q6−2260711q5−1577469q4 + 273280q3 + 1883026q2 + 2187926q + 976970−931323q−1−2157307q−2−1893519q−3−296676q−4 + 1414673q−5 + 2136498q−6 + 1404434q−7−260131q−8−1666401q−9−1908538q−10−843657q−11 + 667373q−12 + 1658528q−13 + 1507905q−14 + 382318q−15−886523q−16−1479924q−17−1046864q−18−30361q−19 + 905971q−20 + 1169119q−21 + 662338q−22−186409q−23−807055q−24−821489q−25−355208q−26 + 263383q−27 + 622264q−28 + 537974q−29 + 145088q−30−263289q−31−421230q−32−312460q−33−34549q−34 + 205459q−35 + 267735q−36 + 157234q−37−20098q−38−133588q−39−149712q−40−70701q−41 + 29488q−42 + 83394q−43 + 72557q−44 + 22346q−45−21110q−46−43985q−47−32343q−48−4874q−49 + 15681q−50 + 19492q−51 + 10333q−52 + 734q−53−8165q−54−8255q−55−2932q−56 + 1772q−57 + 3263q−58 + 2009q−59 + 1067q−60−1037q−61−1411q−62−502q−63 + 221q−64 + 369q−65 + 109q−66 + 266q−67−120q−68−199q−69−16q−70 + 55q−71 + 42q−72−52q−73 + 49q−74−5q−75−34q−76 + 11q−77 + 8q−78 + 7q−79−14q−80 + 3q−81 + 5q−82−4q−83 + q−84

[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.

10_118

10_120

Retrieved from "http://katlas.math.toronto.edu/wiki/10_119"
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