9 49

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9_48

10_1

Contents

Image:9 49.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 9 49's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 9_49's page at Knotilus!

Visit 9 49's page at the original Knot Atlas!

[edit 9 49 Quick Notes]
[edit 9 49 Further Notes and Views]


[edit] Knot presentations

Planar diagram presentation X6271 X12,8,13,7 X5,15,6,14 X3,11,4,10 X11,3,12,2 X15,5,16,4 X17,9,18,8 X9,17,10,16 X18,14,1,13
Gauss code 1, 5, -4, 6, -3, -1, 2, 7, -8, 4, -5, -2, 9, 3, -6, 8, -7, -9
Dowker-Thistlethwaite code 6 -10 -14 12 -16 -2 18 -4 -8
Conway Notation [-20:-20:-20]


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

Length is 11, width is 4,

Braid index is 4

Image:9 49_ML.gif Image:9 49_AP.gif
[{2, 7}, {1, 5}, {8, 3}, {7, 9}, {6, 2}, {4, 1}, {5, 8}, {3, 6}, {9, 4}]

[edit Notes on presentations of 9 49]


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["9 49"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X6271 X12,8,13,7 X5,15,6,14 X3,11,4,10 X11,3,12,2 X15,5,16,4 X17,9,18,8 X9,17,10,16 X18,14,1,13
In[5]:= GaussCode[K]
Out[5]= 1, 5, -4, 6, -3, -1, 2, 7, -8, 4, -5, -2, 9, 3, -6, 8, -7, -9
In[6]:= DTCode[K]
Out[6]= 6 -10 -14 12 -16 -2 18 -4 -8

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [-20:-20:-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,{1,1,2,1,1,−3,2,−1,2,3,3})
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]]
Image:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart2.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:9 49_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{2, 7}, {1, 5}, {8, 3}, {7, 9}, {6, 2}, {4, 1}, {5, 8}, {3, 6}, {9, 4}]
In[14]:= Draw[ap]
Image:9 49_AP.gif
Out[14]= -Graphics-

[edit] Three dimensional invariants

Symmetry type Reversible
Unknotting number 3
3-genus 2
Bridge index 3
Super bridge index {4,5}
Nakanishi index 2
Maximal Thurston-Bennequin number [3][-12]
Hyperbolic Volume 9.42707
A-Polynomial See Data:9 49/A-polynomial

[edit Notes for 9 49's three dimensional invariants]

[edit] Four dimensional invariants

Smooth 4 genus 2
Topological 4 genus 2
Concordance genus 2
Rasmussen s-Invariant -4

[edit Notes for 9 49's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial 3t2−6t + 7−6t−1 + 3t−2
Conway polynomial 3z4 + 6z2 + 1
2nd Alexander ideal (db, data sources) {5,t + 1}
Determinant and Signature { 25, 4 }
Jones polynomial −2q9 + 3q8−4q7 + 5q6−4q5 + 4q4−2q3 + q2
HOMFLY-PT polynomial (db, data sources) z4a−4 + 2z4a−6 + 2z2a−4 + 6z2a−6−2z2a−8 + 4a−6−3a−8
Kauffman polynomial (db, data sources) z7a−7 + z7a−9 + 3z6a−6 + 4z6a−8 + z6a−10 + 2z5a−5 + z5a−7−z5a−9 + z4a−4−8z4a−6−9z4a−8−3z3a−5−3z3a−7 + 3z3a−9 + 3z3a−11−2z2a−4 + 9z2a−6 + 10z2a−8−z2a−10 + 2za−7−2za−9−4za−11−4a−6−3a−8
The A2 invariant q−6−q−8 + q−10 + q−14 + 3q−16 + q−18 + 2q−20−q−22−q−24−q−26−2q−28
The G2 invariant q−30−q−32 + 2q−34−3q−36 + 2q−38−q−40−2q−42 + 8q−44−10q−46 + 12q−48−7q−50−q−52 + 10q−54−16q−56 + 19q−58−11q−60 + q−62 + 10q−64−14q−66 + 13q−68−2q−70−6q−72 + 14q−74−12q−76 + 4q−78 + 9q−80−15q−82 + 21q−84−16q−86 + 9q−88 + 5q−90−13q−92 + 22q−94−22q−96 + 16q−98−4q−100−7q−102 + 13q−104−16q−106 + 9q−108−q−110−10q−112 + 10q−114−11q−116−2q−118 + 10q−120−20q−122 + 16q−124−9q−126−4q−128 + 11q−130−16q−132 + 15q−134−7q−136 + q−138 + 3q−140−7q−142 + 7q−144−2q−146 + q−148 + q−150
Further Quantum Invariants
Further quantum knot invariants for 9_49.

A1 Invariants.

Weight Invariant
1 q−3−q−5 + 2q−7 + q−11 + q−13−q−15 + q−17−2q−19
2 q−6−q−8 + 5q−12−q−14−5q−16 + 5q−18 + 2q−20−5q−22 + 4q−24 + 4q−26−3q−28−q−30 + q−32 + q−34−5q−36 + q−38 + 5q−40−6q−42−2q−44 + 5q−46−3q−48−3q−50 + 3q−52 + q−54
3 q−9−q−11 + 3q−15 + 3q−17−3q−19−7q−21 + 3q−23 + 14q−25 + 4q−27−14q−29−13q−31 + 14q−33 + 18q−35−9q−37−21q−39 + 4q−41 + 23q−43 + q−45−19q−47−3q−49 + 14q−51 + 6q−53−9q−55−9q−57 + 2q−59 + 8q−61 + q−63−14q−65−7q−67 + 14q−69 + 14q−71−16q−73−17q−75 + 12q−77 + 21q−79−6q−81−21q−83−q−85 + 18q−87 + 5q−89−10q−91−7q−93 + 5q−95 + 8q−97−q−99−2q−101−2q−103
4 q−12−q−14 + 3q−18 + q−20 + q−22−6q−24−4q−26 + 8q−28 + 10q−30 + 14q−32−12q−34−28q−36−13q−38 + 12q−40 + 51q−42 + 23q−44−29q−46−58q−48−37q−50 + 56q−52 + 76q−54 + 19q−56−66q−58−93q−60 + 10q−62 + 84q−64 + 69q−66−28q−68−97q−70−28q−72 + 51q−74 + 71q−76 + 4q−78−62q−80−38q−82 + 14q−84 + 45q−86 + 17q−88−25q−90−34q−92−9q−94 + 25q−96 + 32q−98 + 7q−100−43q−102−38q−104 + 13q−106 + 56q−108 + 43q−110−49q−112−73q−114−13q−116 + 71q−118 + 87q−120−25q−122−88q−124−57q−126 + 39q−128 + 99q−130 + 24q−132−50q−134−75q−136−17q−138 + 58q−140 + 45q−142 + 7q−144−37q−146−35q−148 + 5q−150 + 19q−152 + 20q−154−q−156−13q−158−7q−160−3q−162 + 3q−164 + 3q−166 + q−168
5 q−15−q−17 + 3q−21 + q−23−q−25−2q−27−3q−29 + 9q−33 + 14q−35 + 3q−37−10q−39−24q−41−23q−43 + 40q−47 + 59q−49 + 34q−51−28q−53−92q−55−97q−57−27q−59 + 96q−61 + 171q−63 + 117q−65−44q−67−206q−69−231q−71−64q−73 + 197q−75 + 325q−77 + 194q−79−114q−81−363q−83−326q−85−8q−87 + 339q−89 + 402q−91 + 127q−93−257q−95−424q−97−219q−99 + 159q−101 + 387q−103 + 263q−105−72q−107−310q−109−263q−111 + 5q−113 + 228q−115 + 229q−117 + 33q−119−156q−121−183q−123−56q−125 + 92q−127 + 141q−129 + 66q−131−52q−133−117q−135−81q−137 + 20q−139 + 108q−141 + 112q−143 + 16q−145−116q−147−156q−149−50q−151 + 121q−153 + 216q−155 + 116q−157−128q−159−281q−161−184q−163 + 100q−165 + 334q−167 + 279q−169−42q−171−353q−173−359q−175−46q−177 + 317q−179 + 417q−181 + 151q−183−229q−185−414q−187−254q−189 + 106q−191 + 349q−193 + 299q−195 + 25q−197−232q−199−292q−201−124q−203 + 107q−205 + 219q−207 + 160q−209 + 3q−211−120q−213−141q−215−61q−217 + 42q−219 + 82q−221 + 63q−223 + 12q−225−31q−227−46q−229−21q−231 + 3q−233 + 12q−235 + 17q−237 + 8q−239−q−241−4q−243−2q−245−2q−247

A2 Invariants.

Weight Invariant
1,0 q−6−q−8 + q−10 + q−14 + 3q−16 + q−18 + 2q−20−q−22−q−24−q−26−2q−28
1,1 q−12−2q−14 + 4q−16−8q−18 + 19q−20−22q−22 + 36q−24−42q−26 + 48q−28−40q−30 + 34q−32−10q−34−6q−36 + 38q−38−56q−40 + 70q−42−87q−44 + 78q−46−84q−48 + 58q−50−45q−52 + 18q−54 + 10q−56−22q−58 + 45q−60−48q−62 + 48q−64−42q−66 + 25q−68−22q−70 + 10q−72−2q−74 + 2q−76 + 2q−78
2,0 q−12−q−14−q−16 + 3q−18 + 3q−20−q−22−q−24 + 2q−26 + 2q−28−2q−30 + q−32 + 4q−34 + 2q−36 + 3q−38 + 5q−40 + 2q−42−q−44−q−46−2q−48−6q−50−4q−52−q−54−q−56−5q−58−q−60 + q−62 + 3q−70 + q−72 + q−74

A3 Invariants.

Weight Invariant
0,1,0 q−12−q−14 + 2q−18−3q−20 + 2q−22 + 6q−24−2q−26 + 5q−28 + 6q−30 + q−34 + 2q−36−q−38−2q−40−3q−42−3q−46−6q−48 + 2q−50−2q−52−5q−54 + 4q−56 + q−58−q−60 + 3q−62
1,0,0 q−9−q−11 + q−13−q−15 + q−17 + q−19 + 3q−21 + 3q−23 + 2q−25 + 2q−27−q−29−q−31−3q−33−q−35−2q−37

A4 Invariants.

Weight Invariant
0,1,0,0 q−18−q−20 + q−24−q−26−q−28 + 4q−30 + 2q−32−q−34 + 4q−36 + 7q−38 + 3q−40 + 2q−42 + 8q−44 + 8q−46 + 3q−50 + 5q−52−3q−54−6q−56−2q−58−8q−60−13q−62−8q−64−5q−66−6q−68−3q−70 + 6q−72 + 6q−74 + 2q−76 + 3q−78 + 4q−80−q−84
1,0,0,0 q−12−q−14 + q−16−q−18 + q−22 + q−24 + 3q−26 + 3q−28 + 4q−30 + 2q−32 + 2q−34−q−36−q−38−3q−40−3q−42−q−44−2q−46

B2 Invariants.

Weight Invariant
0,1 q−12−q−14 + 2q−16−4q−18 + 5q−20−4q−22 + 4q−24 + 3q−28 + 2q−30−2q−32 + 7q−34−8q−36 + 7q−38−8q−40 + 5q−42−6q−44 + 3q−46−2q−50 + 4q−52−3q−54 + 4q−56−5q−58 + 3q−60−3q−62
1,0 q−18−q−22−q−24 + q−26 + 3q−28−4q−32−q−34 + 5q−36 + 5q−38−2q−40−2q−42 + q−44 + 6q−46 + 2q−48−2q−50−q−52 + 4q−54 + 2q−56−2q−58−2q−60 + q−62 + 3q−64−q−66−4q−68−2q−70 + 2q−72−5q−76−4q−78 + 2q−80 + 3q−82−3q−84−5q−86−q−88 + 4q−90 + 3q−92−2q−94−2q−96 + q−98 + 3q−100

D4 Invariants.

Weight Invariant
1,0,0,0 q−18−q−20 + q−22−2q−24 + 3q−26−4q−28 + 4q−30−2q−32 + 5q−34 + q−36 + 4q−38 + 4q−40 + 5q−42 + 6q−44−2q−46 + 6q−48−5q−50 + 5q−52−8q−54 + 2q−56−8q−58 + 3q−60−5q−62−4q−66−2q−68 + q−70−4q−72 + q−74−4q−76 + 4q−78−2q−80 + 4q−82−2q−84 + 3q−86

G2 Invariants.

Weight Invariant
1,0 q−30−q−32 + 2q−34−3q−36 + 2q−38−q−40−2q−42 + 8q−44−10q−46 + 12q−48−7q−50−q−52 + 10q−54−16q−56 + 19q−58−11q−60 + q−62 + 10q−64−14q−66 + 13q−68−2q−70−6q−72 + 14q−74−12q−76 + 4q−78 + 9q−80−15q−82 + 21q−84−16q−86 + 9q−88 + 5q−90−13q−92 + 22q−94−22q−96 + 16q−98−4q−100−7q−102 + 13q−104−16q−106 + 9q−108−q−110−10q−112 + 10q−114−11q−116−2q−118 + 10q−120−20q−122 + 16q−124−9q−126−4q−128 + 11q−130−16q−132 + 15q−134−7q−136 + q−138 + 3q−140−7q−142 + 7q−144−2q−146 + q−148 + q−150

.

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["9 49"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= 3t2−6t + 7−6t−1 + 3t−2
In[5]:= Conway[K][z]
Out[5]= 3z4 + 6z2 + 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]= {5,t + 1}
In[7]:= {KnotDet[K], KnotSignature[K]}
Out[7]= { 25, 4 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= −2q9 + 3q8−4q7 + 5q6−4q5 + 4q4−2q3 + q2
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= z4a−4 + 2z4a−6 + 2z2a−4 + 6z2a−6−2z2a−8 + 4a−6−3a−8
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= z7a−7 + z7a−9 + 3z6a−6 + 4z6a−8 + z6a−10 + 2z5a−5 + z5a−7−z5a−9 + z4a−4−8z4a−6−9z4a−8−3z3a−5−3z3a−7 + 3z3a−9 + 3z3a−11−2z2a−4 + 9z2a−6 + 10z2a−8−z2a−10 + 2za−7−2za−9−4za−11−4a−6−3a−8

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

Same Alexander/Conway Polynomial: {}

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["9 49"];
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]= { 3t2−6t + 7−6t−1 + 3t−2, −2q9 + 3q8−4q7 + 5q6−4q5 + 4q4−2q3 + q2 }
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] Vassiliev invariants

V2 and V3: (6, 14)
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
24 112 288 700 116 2688 \frac{14368}{3} \frac{2560}{3} 688 2304 6272 16800 2784 \frac{166191}{5} \frac{1876}{5} \frac{207244}{15} \frac{689}{3} \frac{9391}{5}

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 = 4 is the signature of 9 49. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 01234567χ
19       2-2
17      1 1
15     32 -1
13    21  1
11   23   1
9  22    0
7  2     2
512      -1
31       1
Integral Khovanov Homology

(db, data source)

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

[edit] The Coloured Jones Polynomials

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

 n  Jn
2 q26 + 2q25−6q24 + q23 + 10q22−13q21−3q20 + 21q19−17q18−9q17 + 27q16−17q15−11q14 + 25q13−10q12−11q11 + 16q10−3q9−8q8 + 6q7 + q6−2q5 + q4
3 −2q50 + q48 + 9q47−5q46−12q45−2q44 + 24q43 + 8q42−31q41−22q40 + 39q39 + 35q38−40q37−51q36 + 40q35 + 65q34−40q33−72q32 + 33q31 + 80q30−33q29−78q28 + 22q27 + 80q26−18q25−70q24 + 5q23 + 64q22 + 2q21−48q20−14q19 + 39q18 + 14q17−21q16−18q15 + 12q14 + 13q13−3q12−8q11 + q10 + 3q9 + q8−2q7 + q6
4 q82 + 2q81−6q79−4q78−5q77 + 14q76 + 21q75−7q74−18q73−45q72 + 12q71 + 65q70 + 31q69−5q68−120q67−46q66 + 90q65 + 105q64 + 70q63−180q62−142q61 + 59q60 + 168q59 + 182q58−196q57−226q56−q55 + 192q54 + 274q53−183q52−269q51−52q50 + 187q49 + 324q48−158q47−276q46−86q45 + 162q44 + 333q43−116q42−248q41−117q40 + 110q39 + 309q38−50q37−181q36−137q35 + 31q34 + 240q33 + 19q32−84q31−122q30−43q29 + 137q28 + 46q27 + q26−65q25−63q24 + 44q23 + 25q22 + 30q21−13q20−35q19 + 5q18 + 15q16 + 3q15−9q14 + q13−2q12 + 3q11 + q10−2q9 + q8

[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.

9_48

10_1

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