L9a46

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	[edit L9a46 Quick Notes] L9a46 is $9_{10}^{3}$ in the Rolfsen table of links.

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Link Presentations

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Planar diagram presentation	X₆₁₇₂ X_12,6,13,5 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_16,12,17,11 X_18,9,11,10 X_10,17,5,18 X_4,15,1,16
Gauss code	{1, -4, 3, -9}, {2, -1, 5, -3, 7, -8}, {6, -2, 4, -5, 9, -6, 8, -7}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {(u-1)(v-1)^{2}(w-1)^{2}}{{\sqrt {u}}vw}}$ (db)
Jones polynomial	$-q^{-5}+q^{4}+4q^{-4}-4q^{3}-6q^{-3}+7q^{2}+10q^{-2}-9q-10q^{-1}+12$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$-a^{4}z^{2}+a^{4}z^{-2}+2a^{2}z^{4}+z^{4}a^{-2}+3a^{2}z^{2}+z^{2}a^{-2}-2a^{2}z^{-2}-a^{2}-z^{6}-3z^{4}-3z^{2}+z^{-2}+1$ (db)
Kauffman polynomial	$a^{5}z^{5}-a^{5}z^{3}+4a^{4}z^{6}-8a^{4}z^{4}+z^{4}a^{-4}+4a^{4}z^{2}-a^{4}z^{-2}+a^{4}+5a^{3}z^{7}-8a^{3}z^{5}+4z^{5}a^{-3}+2a^{3}z^{3}-3z^{3}a^{-3}-a^{3}z+2a^{3}z^{-1}+2a^{2}z^{8}+8a^{2}z^{6}+7z^{6}a^{-2}-23a^{2}z^{4}-9z^{4}a^{-2}+12a^{2}z^{2}+4z^{2}a^{-2}-2a^{2}z^{-2}+a^{2}+11az^{7}+6z^{7}a^{-1}-17az^{5}-4z^{5}a^{-1}+4az^{3}-2z^{3}a^{-1}-az+2az^{-1}+2z^{8}+11z^{6}-25z^{4}+12z^{2}-z^{-2}+1$ (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		\

-5

-4

-3

-2

-1

0

1

2

3

4

χ

9

1

7

3

-3

5

4

1

3

5

3

-2

1

7

4

3

-1

5

7

2

-3

5

0

-5

3

7

4

-7

1

3

-2

-9

3

-11

1

-1

Integral Khovanov Homology

(db, data source)

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