L11a218

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a218 at Knotilus!
	[edit L11a218 Quick Notes]

[edit L11a218 Further Notes and Views]

Link Presentations

[edit Notes on L11a218's Link Presentations]

Planar diagram presentation	X₈₁₉₂ X_12,4,13,3 X_20,10,21,9 X_22,12,7,11 X_10,22,11,21 X_16,6,17,5 X_18,16,19,15 X_14,20,15,19 X₂₇₃₈ X_4,14,5,13 X_6,18,1,17
Gauss code	{1, -9, 2, -10, 6, -11}, {9, -1, 3, -5, 4, -2, 10, -8, 7, -6, 11, -7, 8, -3, 5, -4}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {2u^{2}v^{4}-3u^{2}v^{3}+3u^{2}v^{2}-3u^{2}v+u^{2}-3uv^{4}+5uv^{3}-5uv^{2}+5uv-3u+v^{4}-3v^{3}+3v^{2}-3v+2}{uv^{2}}}$ (db)
Jones polynomial	$q^{23/2}-3q^{21/2}+6q^{19/2}-10q^{17/2}+13q^{15/2}-14q^{13/2}+14q^{11/2}-12q^{9/2}+8q^{7/2}-6q^{5/2}+2q^{3/2}-{\sqrt {q}}$ (db)
Signature	5 (db)
HOMFLY-PT polynomial	$z^{5}a^{-9}+3z^{3}a^{-9}+2za^{-9}-z^{7}a^{-7}-4z^{5}a^{-7}-5z^{3}a^{-7}-2za^{-7}+a^{-7}z^{-1}-z^{7}a^{-5}-4z^{5}a^{-5}-5z^{3}a^{-5}-4za^{-5}-3a^{-5}z^{-1}+z^{5}a^{-3}+4z^{3}a^{-3}+5za^{-3}+2a^{-3}z^{-1}$ (db)
Kauffman polynomial	$-z^{10}a^{-6}-z^{10}a^{-8}-2z^{9}a^{-5}-6z^{9}a^{-7}-4z^{9}a^{-9}-2z^{8}a^{-4}-3z^{8}a^{-6}-8z^{8}a^{-8}-7z^{8}a^{-10}-z^{7}a^{-3}+3z^{7}a^{-5}+14z^{7}a^{-7}+3z^{7}a^{-9}-7z^{7}a^{-11}+7z^{6}a^{-4}+16z^{6}a^{-6}+29z^{6}a^{-8}+15z^{6}a^{-10}-5z^{6}a^{-12}+5z^{5}a^{-3}+9z^{5}a^{-5}-3z^{5}a^{-7}+8z^{5}a^{-9}+12z^{5}a^{-11}-3z^{5}a^{-13}-5z^{4}a^{-4}-11z^{4}a^{-6}-28z^{4}a^{-8}-16z^{4}a^{-10}+5z^{4}a^{-12}-z^{4}a^{-14}-9z^{3}a^{-3}-17z^{3}a^{-5}-5z^{3}a^{-7}-10z^{3}a^{-9}-10z^{3}a^{-11}+3z^{3}a^{-13}-3z^{2}a^{-4}-2z^{2}a^{-6}+9z^{2}a^{-8}+6z^{2}a^{-10}-z^{2}a^{-12}+z^{2}a^{-14}+7za^{-3}+10za^{-5}+3za^{-7}+2za^{-9}+2za^{-11}+3a^{-4}+3a^{-6}+a^{-8}-2a^{-3}z^{-1}-3a^{-5}z^{-1}-a^{-7}z^{-1}$ (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		\

-2

-1

0

1

2

3

4

5

6

7

8

9

χ

24

1

-1

22

2

20

4

1

-3

18

6

2

4

16

7

4

-3

14

7

6

1

12

7

0

10

5

7

-2

8

4

8

4

6

2

4

-2

4

1

5

4

2

1

-1

0

1

Integral Khovanov Homology

(db, data source)

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