10 153

10_152

10_154

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 10 153's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 153 at Knotilus!

10_153 is not $k$-colourable for any $k$. See The Determinant and the Signature.

Knot presentations

Planar diagram presentation	X4251 X8493 X12,6,13,5 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X6,12,7,11 X2837
Gauss code	1, -10, 2, -1, 3, -9, 10, -2, -5, 6, 9, -3, -4, 8, -7, 5, -6, 4, -8, 7
Dowker-Thistlethwaite code	4 8 12 2 -16 6 -18 -20 -10 -14
Conway Notation	[(3,2)-(21,2)]

Minimum Braid Representative	A Morse Link Presentation	An Arc Presentation
Length is 11, width is 4, Braid index is 4		[{3, 9}, {2, 4}, {1, 3}, {10, 5}, {9, 2}, {11, 6}, {5, 7}, {4, 10}, {6, 8}, {7, 11}, {8, 1}]

[edit Notes on presentations of 10 153]

Knot 10_153.

A graph, knot 10_153.

A part of a knot and a part of a graph.

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["10 153"];

In[4]:=

PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

X4251 X8493 X12,6,13,5 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X6,12,7,11 X2837

In[5]:=

GaussCode[K]

Out[5]=

1, -10, 2, -1, 3, -9, 10, -2, -5, 6, 9, -3, -4, 8, -7, 5, -6, 4, -8, 7

In[6]:=

DTCode[K]

Out[6]=

4 8 12 2 -16 6 -18 -20 -10 -14

(The path below may be different on your system)

In[7]:=

AppendTo[$Path, "C:/bin/LinKnot/"];

In[8]:=

ConwayNotation[K]

Out[8]=

[(3,2)-(21,2)]

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]=

${\textrm {BR}}(4,\{-1,-1,-1,-2,-1,-1,3,2,2,2,3\})$

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[{3, 9}, {2, 4}, {1, 3}, {10, 5}, {9, 2}, {11, 6}, {5, 7}, {4, 10}, {6, 8}, {7, 11}, {8, 1}]

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Chiral Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-4] Hyperbolic Volume 7.37434 A-Polynomial See Data:10 153/A-polynomial

[edit Notes for 10 153's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $0$ Topological 4 genus $0$ Concordance genus $0$ Rasmussen s-Invariant 0

[edit Notes for 10 153's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{3}-t^{2}-t+3-t^{-1}-t^{-2}+t^{-3}$
Conway polynomial	$z^{6}+5z^{4}+4z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 1, 0 }
Jones polynomial	$-q^{4}+q^{3}-q^{2}+q+1+q^{-2}-q^{-3}+q^{-4}-q^{-5}$
HOMFLY-PT polynomial (db, data sources)	$z^{6}-z^{4}a^{-2}+6z^{4}-a^{4}z^{2}-a^{2}z^{2}-4z^{2}a^{-2}+10z^{2}-a^{4}-a^{2}-3a^{-2}+6$
Kauffman polynomial (db, data sources)	$z^{8}a^{-2}+z^{8}+az^{7}+2z^{7}a^{-1}+z^{7}a^{-3}+a^{4}z^{6}-6z^{6}a^{-2}-7z^{6}+a^{5}z^{5}+a^{3}z^{5}-7az^{5}-13z^{5}a^{-1}-6z^{5}a^{-3}-4a^{4}z^{4}+10z^{4}a^{-2}+14z^{4}-4a^{5}z^{3}-4a^{3}z^{3}+12az^{3}+22z^{3}a^{-1}+10z^{3}a^{-3}+3a^{4}z^{2}-2a^{2}z^{2}-7z^{2}a^{-2}-12z^{2}+3a^{5}z+2a^{3}z-6az-10za^{-1}-5za^{-3}-a^{4}+a^{2}+3a^{-2}+6$
The A2 invariant	$-q^{16}-q^{12}-q^{10}+2q^{4}+2q^{2}+3+2q^{-2}-q^{-8}-q^{-10}-q^{-12}$
The G2 invariant	$q^{80}+q^{76}-q^{74}+q^{70}-2q^{68}+q^{64}-3q^{62}+q^{60}-q^{58}-4q^{56}+5q^{54}-5q^{52}+q^{50}+q^{48}-5q^{46}+5q^{44}-3q^{42}-2q^{40}+2q^{38}-4q^{36}+q^{34}+3q^{32}-5q^{30}+3q^{28}-q^{24}+2q^{22}-2q^{20}+2q^{18}+4q^{14}-2q^{12}+3q^{10}+4q^{8}-q^{6}+5q^{4}-q^{2}+2+6q^{-2}-q^{-4}+2q^{-6}+4q^{-8}-2q^{-10}+6q^{-12}-q^{-14}-3q^{-16}+4q^{-18}-4q^{-20}+2q^{-22}-3q^{-26}+q^{-28}-q^{-30}-3q^{-32}-2q^{-36}-q^{-38}-3q^{-42}-q^{-48}-q^{-52}+q^{-56}+q^{-60}$

Further Quantum Invariants

Further quantum knot invariants for 10_153.

A1 Invariants.

Weight	Invariant
1	$-q^{11}+q^{3}+q+2q^{-1}-q^{-9}$
2	$q^{32}-q^{28}+q^{24}-3q^{20}-q^{18}+2q^{16}-2q^{14}-q^{12}+2q^{10}+q^{6}+q^{4}+2q^{2}+1+q^{-2}+2q^{-4}-2q^{-8}+q^{-10}+q^{-12}-2q^{-14}-q^{-16}-q^{-24}+q^{-28}$
3	$-q^{63}+q^{59}+q^{57}-2q^{53}-q^{51}+q^{49}+4q^{47}+3q^{45}-2q^{43}-5q^{41}-2q^{39}+5q^{37}+4q^{35}-4q^{33}-7q^{31}-q^{29}+5q^{27}+q^{25}-4q^{23}-2q^{21}+q^{19}+q^{17}+q^{15}+q^{9}+q^{7}-q^{5}+q^{3}+5q+4q^{-1}-2q^{-3}-3q^{-5}+6q^{-7}+5q^{-9}-3q^{-11}-7q^{-13}-q^{-15}+5q^{-17}+2q^{-19}-3q^{-21}-5q^{-23}-2q^{-25}+3q^{-27}+3q^{-29}-3q^{-33}-2q^{-35}+q^{-37}+q^{-39}+q^{-41}-q^{-47}+q^{-51}+q^{-53}-q^{-57}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{16}-q^{12}-q^{10}+2q^{4}+2q^{2}+3+2q^{-2}-q^{-8}-q^{-10}-q^{-12}$
1,1	$q^{44}+2q^{40}-2q^{38}+2q^{34}-4q^{32}+6q^{30}-8q^{28}+4q^{26}-2q^{24}-4q^{22}+2q^{20}-12q^{18}+4q^{16}-6q^{14}+3q^{12}+6q^{8}+4q^{6}+5q^{4}+8q^{2}+10q^{-2}-2q^{-4}+4q^{-6}-4q^{-10}+4q^{-12}-6q^{-14}-2q^{-16}-2q^{-18}-4q^{-20}+2q^{-22}-4q^{-24}+2q^{-32}+q^{-36}$
2,0	$q^{42}+q^{36}+q^{34}+q^{32}-q^{28}-2q^{26}-5q^{24}-2q^{22}-3q^{20}-3q^{18}-q^{16}+q^{12}+3q^{8}+3q^{6}+6q^{4}+5q^{2}+8+4q^{-2}+2q^{-4}+q^{-6}-2q^{-8}-2q^{-10}-2q^{-12}-2q^{-14}-2q^{-16}-3q^{-18}-2q^{-20}-q^{-22}-q^{-24}+q^{-30}+q^{-32}+q^{-34}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{34}+q^{30}-q^{24}-3q^{22}-q^{20}-3q^{18}-3q^{16}-q^{14}-2q^{12}-2q^{10}+q^{8}+3q^{6}+5q^{4}+8q^{2}+10+7q^{-2}+4q^{-4}-q^{-6}-2q^{-8}-7q^{-10}-5q^{-12}-3q^{-14}-3q^{-16}+q^{-20}+q^{-22}+q^{-26}$
1,0,0	$-q^{21}-q^{17}-q^{15}-q^{13}-q^{11}+2q^{5}+3q^{3}+4q+3q^{-1}+3q^{-3}-q^{-7}-q^{-9}-2q^{-11}-q^{-13}-q^{-15}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{44}+q^{40}+2q^{38}+q^{36}+q^{34}+q^{32}-q^{30}-3q^{28}-3q^{26}-5q^{24}-6q^{22}-7q^{20}-6q^{18}-7q^{16}-8q^{14}-2q^{12}+q^{10}+4q^{8}+13q^{6}+19q^{4}+20q^{2}+20+17q^{-2}+8q^{-4}-8q^{-8}-11q^{-10}-15q^{-12}-13q^{-14}-8q^{-16}-5q^{-18}-2q^{-20}+2q^{-22}+3q^{-24}+2q^{-26}+2q^{-28}+q^{-30}+q^{-32}$
1,0,0,0	$-q^{26}-q^{22}-q^{20}-q^{18}-q^{16}-q^{14}-q^{12}+2q^{6}+3q^{4}+5q^{2}+4+4q^{-2}+3q^{-4}-q^{-8}-2q^{-10}-2q^{-12}-2q^{-14}-q^{-16}-q^{-18}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{34}-q^{30}-q^{24}+q^{22}-q^{20}+q^{18}-q^{16}+q^{14}+q^{8}-q^{6}+3q^{4}+2+q^{-2}+2q^{-4}+q^{-6}+q^{-10}-q^{-12}+q^{-14}-q^{-16}-q^{-20}-q^{-22}-q^{-26}$
1,0	$q^{56}+q^{48}-q^{44}+q^{40}-q^{38}-2q^{36}-q^{34}-q^{30}-3q^{28}-2q^{26}-2q^{20}-q^{18}+q^{14}+q^{12}+q^{10}+2q^{8}+4q^{6}+3q^{4}+4q^{2}+3+4q^{-2}+3q^{-4}+3q^{-6}-q^{-8}-q^{-14}-3q^{-16}-3q^{-18}-q^{-20}-q^{-22}-3q^{-24}-2q^{-26}+q^{-36}+q^{-44}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{46}+q^{42}+q^{38}-2q^{34}-q^{32}-3q^{30}-q^{28}-3q^{26}-q^{24}-3q^{22}-q^{20}-q^{18}-2q^{16}-2q^{14}-2q^{12}+q^{10}+q^{8}+6q^{6}+6q^{4}+10q^{2}+10+10q^{-2}+6q^{-4}+4q^{-6}-4q^{-10}-5q^{-12}-7q^{-14}-5q^{-16}-6q^{-18}-2q^{-20}-2q^{-22}+q^{-26}+q^{-28}+q^{-30}+q^{-34}$

G2 Invariants.

Weight

Invariant

1,0

$q^{80}+q^{76}-q^{74}+q^{70}-2q^{68}+q^{64}-3q^{62}+q^{60}-q^{58}-4q^{56}+5q^{54}-5q^{52}+q^{50}+q^{48}-5q^{46}+5q^{44}-3q^{42}-2q^{40}+2q^{38}-4q^{36}+q^{34}+3q^{32}-5q^{30}+3q^{28}-q^{24}+2q^{22}-2q^{20}+2q^{18}+4q^{14}-2q^{12}+3q^{10}+4q^{8}-q^{6}+5q^{4}-q^{2}+2+6q^{-2}-q^{-4}+2q^{-6}+4q^{-8}-2q^{-10}+6q^{-12}-q^{-14}-3q^{-16}+4q^{-18}-4q^{-20}+2q^{-22}-3q^{-26}+q^{-28}-q^{-30}-3q^{-32}-2q^{-36}-q^{-38}-3q^{-42}-q^{-48}-q^{-52}+q^{-56}+q^{-60}$

.

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["10 153"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

$t^{3}-t^{2}-t+3-t^{-1}-t^{-2}+t^{-3}$

In[5]:=

Conway[K][z]

Out[5]=

$z^{6}+5z^{4}+4z^{2}+1$

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]=

{ 1, 0 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

$-q^{4}+q^{3}-q^{2}+q+1+q^{-2}-q^{-3}+q^{-4}-q^{-5}$

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

$z^{6}-z^{4}a^{-2}+6z^{4}-a^{4}z^{2}-a^{2}z^{2}-4z^{2}a^{-2}+10z^{2}-a^{4}-a^{2}-3a^{-2}+6$

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

$z^{8}a^{-2}+z^{8}+az^{7}+2z^{7}a^{-1}+z^{7}a^{-3}+a^{4}z^{6}-6z^{6}a^{-2}-7z^{6}+a^{5}z^{5}+a^{3}z^{5}-7az^{5}-13z^{5}a^{-1}-6z^{5}a^{-3}-4a^{4}z^{4}+10z^{4}a^{-2}+14z^{4}-4a^{5}z^{3}-4a^{3}z^{3}+12az^{3}+22z^{3}a^{-1}+10z^{3}a^{-3}+3a^{4}z^{2}-2a^{2}z^{2}-7z^{2}a^{-2}-12z^{2}+3a^{5}z+2a^{3}z-6az-10za^{-1}-5za^{-3}-a^{4}+a^{2}+3a^{-2}+6$

"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["10 153"];

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]=

{ $t^{3}-t^{2}-t+3-t^{-1}-t^{-2}+t^{-3}$, $-q^{4}+q^{3}-q^{2}+q+1+q^{-2}-q^{-3}+q^{-4}-q^{-5}$ }

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]=

{}

Vassiliev invariants

V2 and V3:

(4, -1)

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 $16$ $-8$ $128$ ${\frac {488}{3}}$ ${\frac {64}{3}}$ $-128$ $-{\frac {560}{3}}$ $-{\frac {128}{3}}$ $-8$ ${\frac {2048}{3}}$ $32$ ${\frac {7808}{3}}$ ${\frac {1024}{3}}$ ${\frac {41222}{15}}$ ${\frac {464}{5}}$ ${\frac {44528}{45}}$ ${\frac {442}{9}}$ ${\frac {1622}{15}}$

V_2,1 through V_6,9 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.

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (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 10 153. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -5 -4 -3 -2 -1 0 1 2 3 4 5 χ 9                     1 -1 7                       0 5                 1 1   0 3             1 1       0 1           1   1       2 -1         1 3 1         1 -3       1               1 -5       1 1             0 -7   1 1                 0 -9                       0 -11 1                     -1

Integral Khovanov Homology (db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$ $i=-3$ $i=-1$ $i=1$ $r=-5$ ${\mathbb {Z} }$ $r=-4$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-3$ ${\mathbb {Z} }$ $r=-2$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-1$ ${\mathbb {Z} }$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=0$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }^{3}$ ${\mathbb {Z} }$ $r=1$ ${\mathbb {Z} }$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=2$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=3$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=4$ ${\mathbb {Z} }$ $r=5$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$

The Coloured Jones Polynomials

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

$n$	$J_{n}$
2	$q^{13}-q^{12}-q^{11}+2q^{10}-q^{9}-q^{8}+q^{7}-2q^{6}+2q^{5}+q^{4}-5q^{3}+4q^{2}+3q-6+4q^{-1}+4q^{-2}-7q^{-3}+4q^{-4}+3q^{-5}-5q^{-6}+q^{-7}+2q^{-8}-q^{-9}-2q^{-10}+2q^{-12}-q^{-13}-q^{-14}+q^{-15}$
3	$-q^{27}+q^{26}+q^{25}-2q^{23}+2q^{21}-q^{19}+2q^{17}-3q^{16}-2q^{15}+3q^{14}+5q^{13}-3q^{12}-7q^{11}+7q^{9}+2q^{8}-4q^{7}-6q^{6}+q^{5}+6q^{4}+4q^{3}-5q^{2}-8q+7+10q^{-1}-4q^{-2}-12q^{-3}+5q^{-4}+12q^{-5}-4q^{-6}-13q^{-7}+5q^{-8}+13q^{-9}-4q^{-10}-13q^{-11}+2q^{-12}+11q^{-13}+q^{-14}-9q^{-15}-4q^{-16}+5q^{-17}+4q^{-18}-q^{-19}-3q^{-20}-2q^{-21}+q^{-22}+2q^{-23}+2q^{-24}-q^{-25}-2q^{-26}+q^{-28}+q^{-29}-q^{-30}$
4	$q^{46}-q^{45}-q^{44}+3q^{41}-q^{40}-q^{39}-q^{38}-q^{37}+3q^{36}-q^{35}-q^{33}+2q^{32}+3q^{31}-3q^{30}-3q^{29}-5q^{28}+5q^{27}+6q^{26}+3q^{25}-q^{24}-10q^{23}-q^{22}+4q^{20}+6q^{19}+q^{18}+2q^{17}-8q^{16}-10q^{15}-3q^{14}+8q^{13}+17q^{12}+7q^{11}-17q^{10}-22q^{9}-5q^{8}+20q^{7}+32q^{6}-5q^{5}-29q^{4}-24q^{3}+7q^{2}+48q+10-28q^{-1}-34q^{-2}-4q^{-3}+54q^{-4}+14q^{-5}-26q^{-6}-36q^{-7}-7q^{-8}+55q^{-9}+14q^{-10}-26q^{-11}-35q^{-12}-8q^{-13}+53q^{-14}+16q^{-15}-21q^{-16}-36q^{-17}-15q^{-18}+44q^{-19}+21q^{-20}-5q^{-21}-29q^{-22}-26q^{-23}+19q^{-24}+19q^{-25}+16q^{-26}-9q^{-27}-23q^{-28}-4q^{-29}+2q^{-30}+15q^{-31}+7q^{-32}-4q^{-33}-5q^{-34}-6q^{-35}+3q^{-37}+3q^{-38}+2q^{-39}+q^{-40}-3q^{-41}-2q^{-42}-q^{-43}+3q^{-45}-q^{-48}-q^{-49}+q^{-50}$
5	$-q^{70}+q^{69}+q^{68}-q^{65}-2q^{64}+2q^{62}+q^{61}+q^{60}-q^{59}-q^{58}-q^{57}+q^{55}+q^{54}-3q^{53}-q^{52}+2q^{51}+2q^{50}+4q^{49}+2q^{48}-5q^{47}-7q^{46}-3q^{45}+5q^{43}+8q^{42}+4q^{41}-q^{40}-4q^{39}-5q^{38}-6q^{37}-3q^{36}+4q^{34}+11q^{33}+11q^{32}+6q^{31}-8q^{30}-19q^{29}-20q^{28}-6q^{27}+13q^{26}+31q^{25}+26q^{24}+2q^{23}-23q^{22}-41q^{21}-29q^{20}+5q^{19}+37q^{18}+49q^{17}+25q^{16}-20q^{15}-55q^{14}-53q^{13}-14q^{12}+49q^{11}+74q^{10}+40q^{9}-23q^{8}-80q^{7}-75q^{6}+4q^{5}+83q^{4}+87q^{3}+22q^{2}-72q-108-33q^{-1}+73q^{-2}+106q^{-3}+47q^{-4}-66q^{-5}-117q^{-6}-46q^{-7}+68q^{-8}+111q^{-9}+51q^{-10}-65q^{-11}-118q^{-12}-47q^{-13}+68q^{-14}+112q^{-15}+50q^{-16}-65q^{-17}-118q^{-18}-48q^{-19}+67q^{-20}+113q^{-21}+52q^{-22}-59q^{-23}-114q^{-24}-60q^{-25}+48q^{-26}+106q^{-27}+70q^{-28}-25q^{-29}-92q^{-30}-79q^{-31}-5q^{-32}+67q^{-33}+78q^{-34}+33q^{-35}-32q^{-36}-65q^{-37}-49q^{-38}-4q^{-39}+39q^{-40}+48q^{-41}+29q^{-42}-8q^{-43}-33q^{-44}-32q^{-45}-16q^{-46}+10q^{-47}+25q^{-48}+21q^{-49}+6q^{-50}-5q^{-51}-17q^{-52}-13q^{-53}-q^{-54}+2q^{-55}+7q^{-56}+8q^{-57}+2q^{-58}-2q^{-59}-q^{-60}-4q^{-61}-4q^{-62}+q^{-64}+2q^{-65}+2q^{-66}+2q^{-67}-q^{-68}-2q^{-69}-q^{-70}+q^{-73}+q^{-74}-q^{-75}$
6	$q^{99}-q^{98}-q^{97}+q^{94}+3q^{92}-q^{91}-2q^{90}-q^{89}-q^{88}+4q^{85}-q^{84}-2q^{80}+q^{79}+4q^{78}-4q^{77}-2q^{76}-2q^{75}-3q^{73}+6q^{72}+9q^{71}+q^{70}-q^{69}-2q^{68}-5q^{67}-13q^{66}+3q^{64}+3q^{63}+4q^{62}+10q^{61}+8q^{60}-5q^{59}-3q^{57}-11q^{56}-16q^{55}-6q^{54}+3q^{53}+5q^{52}+17q^{51}+28q^{50}+16q^{49}-5q^{48}-20q^{47}-25q^{46}-38q^{45}-24q^{44}+16q^{43}+33q^{42}+46q^{41}+36q^{40}+30q^{39}-28q^{38}-59q^{37}-54q^{36}-50q^{35}-8q^{34}+32q^{33}+99q^{32}+69q^{31}+44q^{30}-8q^{29}-84q^{28}-117q^{27}-106q^{26}+8q^{25}+56q^{24}+146q^{23}+147q^{22}+61q^{21}-73q^{20}-184q^{19}-159q^{18}-119q^{17}+72q^{16}+200q^{15}+236q^{14}+110q^{13}-85q^{12}-214q^{11}-287q^{10}-100q^{9}+110q^{8}+293q^{7}+262q^{6}+75q^{5}-165q^{4}-352q^{3}-225q^{2}-q+276+325q^{-1}+175q^{-2}-116q^{-3}-361q^{-4}-273q^{-5}-54q^{-6}+258q^{-7}+341q^{-8}+208q^{-9}-102q^{-10}-362q^{-11}-281q^{-12}-65q^{-13}+255q^{-14}+343q^{-15}+213q^{-16}-101q^{-17}-363q^{-18}-282q^{-19}-65q^{-20}+255q^{-21}+343q^{-22}+213q^{-23}-102q^{-24}-359q^{-25}-285q^{-26}-70q^{-27}+250q^{-28}+346q^{-29}+226q^{-30}-93q^{-31}-343q^{-32}-298q^{-33}-106q^{-34}+208q^{-35}+337q^{-36}+270q^{-37}-19q^{-38}-269q^{-39}-305q^{-40}-194q^{-41}+69q^{-42}+253q^{-43}+300q^{-44}+121q^{-45}-82q^{-46}-215q^{-47}-241q^{-48}-116q^{-49}+55q^{-50}+195q^{-51}+173q^{-52}+109q^{-53}-15q^{-54}-123q^{-55}-155q^{-56}-97q^{-57}-q^{-58}+51q^{-59}+109q^{-60}+92q^{-61}+39q^{-62}-32q^{-63}-54q^{-64}-64q^{-65}-58q^{-66}-4q^{-67}+28q^{-68}+47q^{-69}+33q^{-70}+30q^{-71}-q^{-72}-27q^{-73}-28q^{-74}-22q^{-75}-8q^{-76}+18q^{-78}+16q^{-79}+10q^{-80}+3q^{-81}-2q^{-82}-7q^{-83}-8q^{-84}-5q^{-85}-2q^{-86}+q^{-87}+2q^{-88}+4q^{-89}+3q^{-90}+3q^{-91}-q^{-92}-q^{-93}-2q^{-94}-2q^{-95}-2q^{-96}+3q^{-98}+q^{-100}-q^{-103}-q^{-104}+q^{-105}$
7	${\textrm {NotAvailable}}(q)$

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.

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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