L11n425

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Link Presentations

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Planar diagram presentation	X₈₁₉₂ X_16,8,17,7 X_5,14,6,15 X_3,10,4,11 X_13,4,14,5 X_17,2,18,3 X_9,19,10,18 X_21,7,22,12 X_11,13,12,22 X_20,16,21,15 X_6,19,1,20
Gauss code	{1, 6, -4, 5, -3, -11}, {2, -1, -7, 4, -9, 8}, {-5, 3, 10, -2, -6, 7, 11, -10, -8, 9}

A Braid Representative	{{{braid_table}}}
A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{-t(1) t(2)^2 t(3)^3+t(1) t(2) t(3)^3-t(2) t(3)^3+t(1) t(2)^2 t(3)^2-t(2)^2 t(3)^2-2 t(1) t(2) t(3)^2+t(2) t(3)^2+t(1)^2 t(3)-t(1) t(3)-t(1)^2 t(2) t(3)+2 t(1) t(2) t(3)+t(1)+t(1)^2 t(2)-t(1) t(2)}{t(1) t(2) t(3)^{3/2}}} (db)
Jones polynomial	$2q^{2}-3q+5-5q^{-1}+6q^{-2}-4q^{-3}+4q^{-4}-2q^{-5}+q^{-6}$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$-a^{2}z^{6}+a^{4}z^{4}-5a^{2}z^{4}+z^{4}+3a^{4}z^{2}-9a^{2}z^{2}+2z^{2}+3a^{4}-6a^{2}+a^{-2}+2+a^{4}z^{-2}-2a^{2}z^{-2}+z^{-2}$ (db)
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^3 z^9+a z^9+3 a^4 z^8+4 a^2 z^8+z^8+2 a^5 z^7-a^3 z^7-3 a z^7+a^6 z^6-14 a^4 z^6-19 a^2 z^6-4 z^6-7 a^5 z^5-8 a^3 z^5+z^5 a^{-1} -4 a^6 z^4+22 a^4 z^4+33 a^2 z^4+7 z^4+4 a^5 z^3+14 a^3 z^3+10 a z^3+3 a^6 z^2-19 a^4 z^2-27 a^2 z^2+2 z^2 a^{-2} -3 z^2-9 a^3 z-9 a z+7 a^4+11 a^2-2 a^{-2} +3+2 a^3 z^{-1} +2 a z^{-1} -a^4 z^{-2} -2 a^2 z^{-2} - z^{-2} } (db)

Khovanov Homology

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

\		r
	\
j		\

-6

-5

-4

-3

-2

-1

0

1

2

χ

5

2

3

2

1

-1

1

3

1

2

-1

4

0

-3

2

1

-5

2

4

2

-7

2

0

-9

2

-11

1

2

-1

-13

1

Integral Khovanov Homology

(db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-1$	$i=1$
$r=-6$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}	${\mathbb {Z} }$
$r=-5$	${\mathbb {Z} }^{2}$
$r=-4$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}}	${\mathbb {Z} }^{2}$
$r=-3$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-2$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-1$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{4}$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}}
$r=0$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2}	${\mathbb {Z} }^{3}$
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=1}	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=2$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}\oplus{\mathbb Z}_2}	${\mathbb {Z} }^{2}$