7 1

6_3

7_2

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 7 1's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 7 1 at Knotilus!
	7_1 should perhaps be called "The Septafoil Knot", following the trefoil knot and the cinquefoil knot. See also T(7,2).

Interlaced form of 7/2 star polygon or "septagram"		Decorative interlaced form of 7/2 star polygon or "septagram"		3D depiction
Heptagram of intersecting circles.

Knot presentations

Planar diagram presentation	X1829 X3,10,4,11 X5,12,6,13 X7,14,8,1 X9,2,10,3 X11,4,12,5 X13,6,14,7
Gauss code	-1, 5, -2, 6, -3, 7, -4, 1, -5, 2, -6, 3, -7, 4
Dowker-Thistlethwaite code	8 10 12 14 2 4 6
Conway Notation	[7]

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

[edit Notes on presentations of 7 1]

Knot 7_1.

A graph, knot 7_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.org/wiki/KnotTheory.

In[3]:=

K = Knot["7 1"];

In[4]:=

PD[K]

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

Out[4]=

X1829 X3,10,4,11 X5,12,6,13 X7,14,8,1 X9,2,10,3 X11,4,12,5 X13,6,14,7

In[5]:=

GaussCode[K]

Out[5]=

-1, 5, -2, 6, -3, 7, -4, 1, -5, 2, -6, 3, -7, 4

In[6]:=

DTCode[K]

Out[6]=

8 10 12 14 2 4 6

(The path below may be different on your system)

In[7]:=

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

In[8]:=

ConwayNotation[K]

Out[8]=

[7]

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]=

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

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]=

{ 2, 7, 2 }

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

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Reversible Unknotting number 3 3-genus 3 Bridge index 2 Super bridge index 4 Nakanishi index 1 Maximal Thurston-Bennequin number Failed to parse (syntax error): {\displaystyle \text{$\$$Failed}} Hyperbolic Volume Not hyperbolic A-Polynomial See Data:7 1/A-polynomial

[edit Notes for 7 1's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $3$ Topological 4 genus $3$ Concordance genus ${\textrm {ConcordanceGenus}}({\textrm {Knot}}(7,1))$ Rasmussen s-Invariant -6

[edit Notes for 7 1's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{3}+t^{-3}-t^{2}-t^{-2}+t+t^{-1}-1$
Conway polynomial	$z^{6}+5z^{4}+6z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 7, -6 }
Jones polynomial	$-q^{-10}+q^{-9}-q^{-8}+q^{-7}-q^{-6}+q^{-5}+q^{-3}$
HOMFLY-PT polynomial (db, data sources)	$a^{8}\left(-z^{4}\right)-4a^{8}z^{2}-3a^{8}+a^{6}z^{6}+6a^{6}z^{4}+10a^{6}z^{2}+4a^{6}$
Kauffman polynomial (db, data sources)	$a^{13}z+a^{12}z^{2}+a^{11}z^{3}-a^{11}z+a^{10}z^{4}-2a^{10}z^{2}+a^{9}z^{5}-3a^{9}z^{3}+a^{9}z+a^{8}z^{6}-5a^{8}z^{4}+7a^{8}z^{2}-3a^{8}+a^{7}z^{5}-4a^{7}z^{3}+3a^{7}z+a^{6}z^{6}-6a^{6}z^{4}+10a^{6}z^{2}-4a^{6}$
The A2 invariant	$-q^{30}-q^{28}-q^{26}+q^{18}+q^{16}+2q^{14}+q^{12}+q^{10}$
The G2 invariant	$q^{168}-q^{136}-q^{134}-q^{128}-q^{126}-q^{124}-q^{118}-q^{116}-q^{102}-q^{96}-q^{94}-q^{92}+q^{88}-2q^{84}+2q^{80}+q^{78}+q^{72}+3q^{70}+2q^{68}+q^{64}+2q^{62}+2q^{60}+q^{58}+q^{54}+q^{52}+q^{50}$

Further Quantum Invariants

Further quantum knot invariants for 7_1.

A1 Invariants.

Weight	Invariant
1	$-q^{21}+q^{9}+q^{7}+q^{5}$
2	$q^{56}-q^{44}-q^{42}-q^{40}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}$
3	$-q^{105}+q^{93}+q^{91}+q^{89}-q^{67}-q^{65}-q^{63}-q^{61}-q^{59}+q^{27}+q^{25}+q^{23}+q^{21}+q^{19}+q^{17}+q^{15}$
4	$q^{168}-q^{156}-q^{154}-q^{152}+q^{130}+q^{128}+q^{126}+q^{124}+q^{122}-q^{90}-q^{88}-q^{86}-q^{84}-q^{82}-q^{80}-q^{78}+q^{36}+q^{34}+q^{32}+q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}$
5	$-q^{245}+q^{233}+q^{231}+q^{229}-q^{207}-q^{205}-q^{203}-q^{201}-q^{199}+q^{167}+q^{165}+q^{163}+q^{161}+q^{159}+q^{157}+q^{155}-q^{113}-q^{111}-q^{109}-q^{107}-q^{105}-q^{103}-q^{101}-q^{99}-q^{97}+q^{45}+q^{43}+q^{41}+q^{39}+q^{37}+q^{35}+q^{33}+q^{31}+q^{29}+q^{27}+q^{25}$
6	$q^{336}-q^{324}-q^{322}-q^{320}+q^{298}+q^{296}+q^{294}+q^{292}+q^{290}-q^{258}-q^{256}-q^{254}-q^{252}-q^{250}-q^{248}-q^{246}+q^{204}+q^{202}+q^{200}+q^{198}+q^{196}+q^{194}+q^{192}+q^{190}+q^{188}-q^{136}-q^{134}-q^{132}-q^{130}-q^{128}-q^{126}-q^{124}-q^{122}-q^{120}-q^{118}-q^{116}+q^{54}+q^{52}+q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+q^{40}+q^{38}+q^{36}+q^{34}+q^{32}+q^{30}$
8	$q^{560}-q^{548}-q^{546}-q^{544}+q^{522}+q^{520}+q^{518}+q^{516}+q^{514}-q^{482}-q^{480}-q^{478}-q^{476}-q^{474}-q^{472}-q^{470}+q^{428}+q^{426}+q^{424}+q^{422}+q^{420}+q^{418}+q^{416}+q^{414}+q^{412}-q^{360}-q^{358}-q^{356}-q^{354}-q^{352}-q^{350}-q^{348}-q^{346}-q^{344}-q^{342}-q^{340}+q^{278}+q^{276}+q^{274}+q^{272}+q^{270}+q^{268}+q^{266}+q^{264}+q^{262}+q^{260}+q^{258}+q^{256}+q^{254}-q^{182}-q^{180}-q^{178}-q^{176}-q^{174}-q^{172}-q^{170}-q^{168}-q^{166}-q^{164}-q^{162}-q^{160}-q^{158}-q^{156}-q^{154}+q^{72}+q^{70}+q^{68}+q^{66}+q^{64}+q^{62}+q^{60}+q^{58}+q^{56}+q^{54}+q^{52}+q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+q^{40}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{30}-q^{28}-q^{26}+q^{18}+q^{16}+2q^{14}+q^{12}+q^{10}$
1,1	$q^{84}-2q^{48}-2q^{46}-4q^{44}-4q^{42}-4q^{40}-2q^{38}-q^{36}+2q^{34}+4q^{32}+4q^{30}+5q^{28}+4q^{26}+4q^{24}+2q^{22}+q^{20}$
2,0	$q^{74}+q^{72}+2q^{70}+q^{68}+q^{66}-q^{62}-2q^{60}-3q^{58}-3q^{56}-3q^{54}-2q^{52}-q^{50}+q^{36}+q^{34}+2q^{32}+2q^{30}+3q^{28}+2q^{26}+2q^{24}+q^{22}+q^{20}$
3,0	$-q^{132}-q^{130}-2q^{128}-2q^{126}-2q^{124}-q^{122}+2q^{118}+4q^{116}+4q^{114}+5q^{112}+4q^{110}+4q^{108}+2q^{106}+q^{104}-q^{94}-2q^{92}-3q^{90}-4q^{88}-5q^{86}-5q^{84}-5q^{82}-4q^{80}-3q^{78}-2q^{76}-q^{74}+q^{54}+q^{52}+2q^{50}+2q^{48}+3q^{46}+3q^{44}+4q^{42}+3q^{40}+3q^{38}+2q^{36}+2q^{34}+q^{32}+q^{30}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{70}-q^{48}-2q^{46}-3q^{44}-3q^{42}-3q^{40}-2q^{38}+q^{34}+3q^{32}+3q^{30}+4q^{28}+3q^{26}+3q^{24}+q^{22}+q^{20}$
1,0,0	$-q^{39}-q^{37}-2q^{35}-q^{33}-q^{31}+q^{27}+q^{25}+2q^{23}+2q^{21}+2q^{19}+q^{17}+q^{15}$
1,0,1	$q^{112}+q^{78}+q^{76}+3q^{74}+3q^{72}+4q^{70}+3q^{68}+q^{66}-3q^{64}-7q^{62}-10q^{60}-14q^{58}-14q^{56}-13q^{54}-8q^{52}-3q^{50}+3q^{48}+8q^{46}+11q^{44}+12q^{42}+11q^{40}+10q^{38}+7q^{36}+5q^{34}+2q^{32}+q^{30}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{88}+q^{86}+q^{84}+q^{82}+q^{80}-q^{66}-2q^{64}-4q^{62}-5q^{60}-7q^{58}-7q^{56}-6q^{54}-4q^{52}-q^{50}+2q^{48}+5q^{46}+6q^{44}+8q^{42}+6q^{40}+6q^{38}+4q^{36}+3q^{34}+q^{32}+q^{30}$
1,0,0,0	$-q^{48}-q^{46}-2q^{44}-2q^{42}-2q^{40}-q^{38}+q^{34}+2q^{32}+2q^{30}+3q^{28}+2q^{26}+2q^{24}+q^{22}+q^{20}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{70}-q^{48}-q^{44}-q^{42}-q^{40}+q^{34}+q^{32}+q^{30}+2q^{28}+q^{26}+q^{24}+q^{22}+q^{20}$
1,0	$q^{112}-q^{78}-q^{76}-q^{74}-q^{72}-2q^{70}-q^{68}-q^{66}-q^{64}-q^{62}+q^{54}+q^{50}+q^{48}+2q^{46}+q^{44}+2q^{42}+q^{40}+2q^{38}+q^{36}+q^{34}+q^{30}$

D4 Invariants.

Weight	Invariant
0,1,0,0	$q^{168}-q^{136}-q^{134}-3q^{132}-3q^{130}-4q^{128}-4q^{126}-q^{124}+3q^{120}+8q^{118}+11q^{116}+12q^{114}+15q^{112}+12q^{110}+12q^{108}+9q^{106}+6q^{104}+2q^{102}-6q^{98}-10q^{96}-16q^{94}-22q^{92}-27q^{90}-32q^{88}-33q^{86}-32q^{84}-27q^{82}-19q^{80}-8q^{78}+12q^{74}+19q^{72}+24q^{70}+26q^{68}+27q^{66}+22q^{64}+20q^{62}+14q^{60}+10q^{58}+6q^{56}+4q^{54}+q^{52}+q^{50}$
1,0,0,0	$q^{98}-q^{66}-q^{64}-3q^{62}-3q^{60}-4q^{58}-4q^{56}-3q^{54}-2q^{52}-q^{50}+2q^{48}+3q^{46}+4q^{44}+5q^{42}+4q^{40}+4q^{38}+3q^{36}+2q^{34}+q^{32}+q^{30}$

G2 Invariants.

Weight	Invariant
1,0	$q^{168}-q^{136}-q^{134}-q^{128}-q^{126}-q^{124}-q^{118}-q^{116}-q^{102}-q^{96}-q^{94}-q^{92}+q^{88}-2q^{84}+2q^{80}+q^{78}+q^{72}+3q^{70}+2q^{68}+q^{64}+2q^{62}+2q^{60}+q^{58}+q^{54}+q^{52}+q^{50}$

.

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["7 1"];

In[4]:=

Alexander[K][t]

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

Out[4]=

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

In[5]:=

Conway[K][z]

Out[5]=

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

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]=

{ 7, -6 }

In[8]:=

Jones[K][q]

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

Out[8]=

$-q^{-10}+q^{-9}-q^{-8}+q^{-7}-q^{-6}+q^{-5}+q^{-3}$

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

$a^{8}\left(-z^{4}\right)-4a^{8}z^{2}-3a^{8}+a^{6}z^{6}+6a^{6}z^{4}+10a^{6}z^{2}+4a^{6}$

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

$a^{13}z+a^{12}z^{2}+a^{11}z^{3}-a^{11}z+a^{10}z^{4}-2a^{10}z^{2}+a^{9}z^{5}-3a^{9}z^{3}+a^{9}z+a^{8}z^{6}-5a^{8}z^{4}+7a^{8}z^{2}-3a^{8}+a^{7}z^{5}-4a^{7}z^{3}+3a^{7}z+a^{6}z^{6}-6a^{6}z^{4}+10a^{6}z^{2}-4a^{6}$

"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["7 1"];

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]=

{ $t^{3}+t^{-3}-t^{2}-t^{-2}+t+t^{-1}-1$, $-q^{-10}+q^{-9}-q^{-8}+q^{-7}-q^{-6}+q^{-5}+q^{-3}$ }

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:

(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 $24$ $-112$ $288$ $684$ $100$ $-2688$ $-{\frac {13888}{3}}$ $-{\frac {2464}{3}}$ $-560$ $2304$ $6272$ $16416$ $2400$ ${\frac {160231}{5}}$ ${\frac {21548}{15}}$ ${\frac {58148}{5}}$ $163$ ${\frac {7351}{5}}$

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 $s=$-6 is the signature of 7 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -7 -6 -5 -4 -3 -2 -1 0 χ -5               1 1 -7               1 1 -9           1     1 -11                 0 -13       1 1       0 -15                 0 -17   1 1           0 -19                 0 -21 1               -1

Integral Khovanov Homology (db, data source)

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

The Coloured Jones Polynomials

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

$n$	$J_{n}$
2	$q^{-6}+q^{-9}-q^{-11}+q^{-12}-q^{-14}+q^{-15}-q^{-17}+q^{-18}-q^{-20}-q^{-23}+q^{-24}-q^{-26}+q^{-27}$
3	$q^{-9}+q^{-13}-q^{-16}+q^{-17}-q^{-20}+q^{-21}-q^{-24}+q^{-25}-q^{-28}+q^{-29}-q^{-31}-q^{-32}+q^{-33}-q^{-35}+q^{-37}-q^{-39}+q^{-41}-q^{-43}+q^{-45}+q^{-46}-q^{-47}+q^{-50}-q^{-51}$
4	$q^{-12}+q^{-17}-q^{-21}+q^{-22}-q^{-26}+q^{-27}-q^{-31}+q^{-32}-q^{-36}+q^{-37}-2q^{-41}+q^{-42}-2q^{-46}+q^{-47}+q^{-48}-2q^{-51}+q^{-52}+q^{-53}-2q^{-56}+q^{-57}+q^{-58}-2q^{-61}+q^{-62}+2q^{-63}-2q^{-66}+q^{-67}+q^{-68}-2q^{-71}+q^{-72}+q^{-73}-2q^{-76}+q^{-77}-q^{-81}+q^{-82}$
5	$q^{-15}+q^{-21}-q^{-26}+q^{-27}-q^{-32}+q^{-33}-q^{-38}+q^{-39}-q^{-44}+q^{-45}-q^{-50}-q^{-56}+q^{-60}-q^{-62}+q^{-66}-q^{-68}+q^{-72}-q^{-74}+q^{-78}+q^{-84}-q^{-87}+q^{-90}-q^{-93}+q^{-96}-q^{-99}-q^{-105}+q^{-107}-q^{-111}+q^{-113}+q^{-119}-q^{-120}$
6	$q^{-18}+q^{-25}-q^{-31}+q^{-32}-q^{-38}+q^{-39}-q^{-45}+q^{-46}-q^{-52}+q^{-53}-q^{-59}+q^{-60}-q^{-61}-q^{-66}+q^{-67}-q^{-68}+q^{-72}-q^{-73}+q^{-74}-q^{-75}+q^{-79}-q^{-80}+q^{-81}-q^{-82}+q^{-86}-q^{-87}+q^{-88}-q^{-89}+q^{-93}-q^{-94}+q^{-95}-q^{-96}+q^{-97}+q^{-100}-q^{-101}+q^{-102}-q^{-103}+q^{-104}-q^{-106}+q^{-107}-q^{-108}+q^{-109}-q^{-110}+q^{-111}-q^{-113}+q^{-114}-q^{-115}+q^{-116}-q^{-117}+q^{-118}-q^{-120}+q^{-121}-q^{-122}+q^{-123}-q^{-124}+q^{-125}-q^{-126}-q^{-127}+q^{-128}-q^{-129}+q^{-130}-q^{-131}+q^{-132}-q^{-134}+q^{-135}-q^{-136}+q^{-137}-q^{-138}+q^{-139}-q^{-141}+q^{-142}-q^{-143}+q^{-144}-q^{-145}+q^{-146}+q^{-149}-q^{-150}+q^{-151}-q^{-152}+q^{-156}-q^{-157}+q^{-158}-q^{-159}-q^{-164}+q^{-165}$
7	$q^{-21}+q^{-29}-q^{-36}+q^{-37}-q^{-44}+q^{-45}-q^{-52}+q^{-53}-q^{-60}+q^{-61}-q^{-68}+q^{-69}-q^{-71}-q^{-76}+q^{-77}-q^{-79}+q^{-85}-q^{-87}+q^{-93}-q^{-95}+q^{-101}-q^{-103}+q^{-109}-q^{-111}+q^{-114}+q^{-117}-q^{-119}+q^{-122}-q^{-127}+q^{-130}-q^{-135}+q^{-138}-q^{-143}+q^{-146}-q^{-150}-q^{-151}+q^{-154}-q^{-158}+q^{-162}-q^{-166}+q^{-170}-q^{-174}+q^{-178}+q^{-179}-q^{-182}+q^{-187}-q^{-190}+q^{-195}-q^{-198}-q^{-201}+q^{-203}-q^{-209}+q^{-211}+q^{-216}-q^{-217}$

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.

6_3 7_2