L11a106

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a106 at Knotilus!
	[edit L11a106 Quick Notes]

[edit L11a106 Further Notes and Views]

Link Presentations

[edit Notes on L11a106's Link Presentations]

Planar diagram presentation	X₆₁₇₂ X_14,3,15,4 X_16,8,17,7 X_22,18,5,17 X_18,9,19,10 X_8,21,9,22 X_20,11,21,12 X_10,19,11,20 X_12,16,13,15 X₂₅₃₆ X_4,13,1,14
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -6, 5, -8, 7, -9, 11, -2, 9, -3, 4, -5, 8, -7, 6, -4}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {uv^{5}-4uv^{4}+8uv^{3}-8uv^{2}+6uv-2u-2v^{5}+6v^{4}-8v^{3}+8v^{2}-4v+1}{{\sqrt {u}}v^{5/2}}}$ (db)
Jones polynomial	$q^{3/2}-4{\sqrt {q}}+{\frac {7}{\sqrt {q}}}-{\frac {12}{q^{3/2}}}+{\frac {16}{q^{5/2}}}-{\frac {19}{q^{7/2}}}+{\frac {18}{q^{9/2}}}-{\frac {16}{q^{11/2}}}+{\frac {12}{q^{13/2}}}-{\frac {7}{q^{15/2}}}+{\frac {3}{q^{17/2}}}-{\frac {1}{q^{19/2}}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$a^{9}z+a^{9}z^{-1}-3a^{7}z^{3}-6a^{7}z-3a^{7}z^{-1}+3a^{5}z^{5}+9a^{5}z^{3}+9a^{5}z+4a^{5}z^{-1}-a^{3}z^{7}-4a^{3}z^{5}-7a^{3}z^{3}-6a^{3}z-2a^{3}z^{-1}+az^{5}+2az^{3}$ (db)
Kauffman polynomial	$-z^{5}a^{11}+2z^{3}a^{11}-za^{11}-3z^{6}a^{10}+5z^{4}a^{10}-3z^{2}a^{10}+a^{10}-5z^{7}a^{9}+7z^{5}a^{9}-4z^{3}a^{9}+2za^{9}-a^{9}z^{-1}-5z^{8}a^{8}+2z^{6}a^{8}+7z^{4}a^{8}-8z^{2}a^{8}+3a^{8}-3z^{9}a^{7}-7z^{7}a^{7}+22z^{5}a^{7}-22z^{3}a^{7}+12za^{7}-3a^{7}z^{-1}-z^{10}a^{6}-10z^{8}a^{6}+18z^{6}a^{6}-6z^{4}a^{6}-5z^{2}a^{6}+3a^{6}-7z^{9}a^{5}+4z^{7}a^{5}+17z^{5}a^{5}-26z^{3}a^{5}+17za^{5}-4a^{5}z^{-1}-z^{10}a^{4}-11z^{8}a^{4}+30z^{6}a^{4}-22z^{4}a^{4}+2z^{2}a^{4}+2a^{4}-4z^{9}a^{3}+2z^{7}a^{3}+14z^{5}a^{3}-17z^{3}a^{3}+8za^{3}-2a^{3}z^{-1}-6z^{8}a^{2}+16z^{6}a^{2}-12z^{4}a^{2}+2z^{2}a^{2}-4z^{7}a+11z^{5}a-7z^{3}a-z^{6}+2z^{4}$ (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		\

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

χ

4

1

-1

2

3

0

4

1

-3

-2

8

3

5

-4

9

5

-4

-6

10

7

3

-8

8

9

1

-10

8

10

-2

-12

5

9

4

-14

2

7

-5

-16

1

5

4

-18

2

-2

-20

1

Integral Khovanov Homology

(db, data source)

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