L11a332

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Planar diagram presentation	X_10,1,11,2 X_2,11,3,12 X_12,3,13,4 X_20,5,21,6 X_22,13,9,14 X_18,21,19,22 X_16,7,17,8 X_14,17,15,18 X_8,9,1,10 X_6,15,7,16 X_4,19,5,20
Gauss code	{1, -2, 3, -11, 4, -10, 7, -9}, {9, -1, 2, -3, 5, -8, 10, -7, 8, -6, 11, -4, 6, -5}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {3t(2)^{3}t(1)^{3}-3t(2)^{2}t(1)^{3}+t(2)t(1)^{3}-3t(2)^{3}t(1)^{2}+8t(2)^{2}t(1)^{2}-5t(2)t(1)^{2}+t(1)^{2}+t(2)^{3}t(1)-5t(2)^{2}t(1)+8t(2)t(1)-3t(1)+t(2)^{2}-3t(2)+3}{t(1)^{3/2}t(2)^{3/2}}}$ (db)
Jones polynomial	${\frac {2}{q^{9/2}}}-{\frac {1}{q^{7/2}}}+{\frac {1}{q^{29/2}}}-{\frac {4}{q^{27/2}}}+{\frac {7}{q^{25/2}}}-{\frac {11}{q^{23/2}}}+{\frac {14}{q^{21/2}}}-{\frac {15}{q^{19/2}}}+{\frac {15}{q^{17/2}}}-{\frac {12}{q^{15/2}}}+{\frac {8}{q^{13/2}}}-{\frac {6}{q^{11/2}}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$a^{13}\left(-z^{3}\right)-2a^{13}z+3a^{11}z^{5}+11a^{11}z^{3}+9a^{11}z-2a^{9}z^{7}-10a^{9}z^{5}-15a^{9}z^{3}-6a^{9}z+a^{9}z^{-1}-a^{7}z^{7}-5a^{7}z^{5}-8a^{7}z^{3}-5a^{7}z-a^{7}z^{-1}$ (db)
Kauffman polynomial	$a^{18}z^{4}+4a^{17}z^{5}-3a^{17}z^{3}+7a^{16}z^{6}-7a^{16}z^{4}+a^{16}z^{2}+8a^{15}z^{7}-8a^{15}z^{5}-a^{15}z^{3}+2a^{15}z+7a^{14}z^{8}-8a^{14}z^{6}+a^{14}z^{4}+4a^{13}z^{9}-12a^{13}z^{5}+7a^{13}z^{3}+a^{13}z+a^{12}z^{10}+10a^{12}z^{8}-37a^{12}z^{6}+42a^{12}z^{4}-18a^{12}z^{2}+7a^{11}z^{9}-20a^{11}z^{7}+18a^{11}z^{5}-12a^{11}z^{3}+7a^{11}z+a^{10}z^{10}+5a^{10}z^{8}-29a^{10}z^{6}+38a^{10}z^{4}-16a^{10}z^{2}+3a^{9}z^{9}-11a^{9}z^{7}+13a^{9}z^{5}-9a^{9}z^{3}+3a^{9}z+a^{9}z^{-1}+2a^{8}z^{8}-7a^{8}z^{6}+5a^{8}z^{4}+a^{8}z^{2}-a^{8}+a^{7}z^{7}-5a^{7}z^{5}+8a^{7}z^{3}-5a^{7}z+a^{7}z^{-1}$ (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		\

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

χ

-6

1

-8

2

1

-1

-10

4

-12

4

2

-2

-14

8

4

-16

7

4

-3

-18

8

0

-20

6

7

1

-22

5

8

-3

-24

3

7

4

-26

1

4

-3

-28

3

-30

1

-1

Integral Khovanov Homology

(db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-8$	$i=-6$
$r=-11$	${\mathbb {Z} }$
$r=-10$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-9$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{3}$	${\mathbb {Z} }^{3}$
$r=-8$	${\mathbb {Z} }^{7}\oplus {\mathbb {Z} }_{2}^{4}$	${\mathbb {Z} }^{5}$
$r=-7$	${\mathbb {Z} }^{8}\oplus {\mathbb {Z} }_{2}^{6}$	${\mathbb {Z} }^{6}$
$r=-6$	${\mathbb {Z} }^{7}\oplus {\mathbb {Z} }_{2}^{8}$	${\mathbb {Z} }^{8}$
$r=-5$	${\mathbb {Z} }^{8}\oplus {\mathbb {Z} }_{2}^{7}$	${\mathbb {Z} }^{7}$
$r=-4$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{8}$	${\mathbb {Z} }^{8}$
$r=-3$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{4}$	${\mathbb {Z} }^{4}$
$r=-2$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{4}$	${\mathbb {Z} }^{4}$
$r=-1$	${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=0$	${\mathbb {Z} }$	${\mathbb {Z} }$