L11a192

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a192 at Knotilus!
	[edit L11a192 Quick Notes]

[edit L11a192 Further Notes and Views]

Link Presentations

[edit Notes on L11a192's Link Presentations]

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

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

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {3t(2)t(1)^{2}-3t(1)^{2}+3t(2)^{2}t(1)-7t(2)t(1)+3t(1)-3t(2)^{2}+3t(2)}{t(1)t(2)}}$ (db)
Jones polynomial	$-{\frac {7}{q^{9/2}}}+{\frac {7}{q^{7/2}}}-{\frac {7}{q^{5/2}}}-q^{3/2}+{\frac {5}{q^{3/2}}}+{\frac {1}{q^{19/2}}}-{\frac {2}{q^{17/2}}}+{\frac {3}{q^{15/2}}}-{\frac {5}{q^{13/2}}}+{\frac {6}{q^{11/2}}}+2{\sqrt {q}}-{\frac {4}{\sqrt {q}}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$-za^{9}+z^{3}a^{7}+2z^{3}a^{5}+za^{5}+2z^{3}a^{3}+za^{3}+a^{3}z^{-1}+z^{3}a-za-az^{-1}-za^{-1}$ (db)
Kauffman polynomial	$-z^{8}a^{10}+6z^{6}a^{10}-11z^{4}a^{10}+6z^{2}a^{10}-2z^{9}a^{9}+12z^{7}a^{9}-23z^{5}a^{9}+16z^{3}a^{9}-3za^{9}-z^{10}a^{8}+3z^{8}a^{8}+3z^{6}a^{8}-11z^{4}a^{8}+4z^{2}a^{8}-4z^{9}a^{7}+19z^{7}a^{7}-26z^{5}a^{7}+12z^{3}a^{7}-2za^{7}-z^{10}a^{6}+z^{8}a^{6}+7z^{6}a^{6}-8z^{4}a^{6}+z^{2}a^{6}-2z^{9}a^{5}+4z^{7}a^{5}+3z^{5}a^{5}-4z^{3}a^{5}+za^{5}-3z^{8}a^{4}+7z^{6}a^{4}-4z^{4}a^{4}+3z^{2}a^{4}-3z^{7}a^{3}+3z^{5}a^{3}+4z^{3}a^{3}-4za^{3}+a^{3}z^{-1}-3z^{6}a^{2}+2z^{4}a^{2}+z^{2}a^{2}-a^{2}-3z^{5}a+3z^{3}a-3za+az^{-1}-2z^{4}+z^{2}-z^{3}a^{-1}+za^{-1}$ (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		\

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

χ

4

1

2

1

-1

0

3

1

2

-2

3

2

-1

-4

4

2

-6

4

0

-8

3

0

-10

3

4

1

-12

2

3

-1

-14

1

3

2

-16

1

2

-1

-18

1

-20

1

-1

Integral Khovanov Homology

(db, data source)

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