L10a46

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L10a46 at Knotilus!
	[edit L10a46 Quick Notes]

[edit L10a46 Further Notes and Views]

Depiction obtained by knotilus

Link Presentations

[edit Notes on L10a46's Link Presentations]

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

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {\left(t(2)^{2}-t(2)+1\right)\left(t(1)t(2)^{3}-2t(2)^{3}-t(1)t(2)^{2}+t(2)^{2}+t(1)t(2)-t(2)-2t(1)+1\right)}{{\sqrt {t(1)}}t(2)^{5/2}}}$ (db)
Jones polynomial	$9q^{9/2}-9q^{7/2}+10q^{5/2}-{\frac {1}{q^{5/2}}}-9q^{3/2}+{\frac {1}{q^{3/2}}}-q^{15/2}+3q^{13/2}-6q^{11/2}+6{\sqrt {q}}-{\frac {5}{\sqrt {q}}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$-z^{5}a^{-5}-3z^{3}a^{-5}-3za^{-5}-a^{-5}z^{-1}+z^{7}a^{-3}+5z^{5}a^{-3}+10z^{3}a^{-3}+11za^{-3}+5a^{-3}z^{-1}-2z^{5}a^{-1}+az^{3}-9z^{3}a^{-1}+4az-14za^{-1}+4az^{-1}-8a^{-1}z^{-1}$ (db)
Kauffman polynomial	$z^{3}a^{-9}+3z^{4}a^{-8}+6z^{5}a^{-7}-4z^{3}a^{-7}+za^{-7}+9z^{6}a^{-6}-15z^{4}a^{-6}+9z^{2}a^{-6}-2a^{-6}+8z^{7}a^{-5}-14z^{5}a^{-5}+4z^{3}a^{-5}+a^{-5}z^{-1}+4z^{8}a^{-4}-22z^{4}a^{-4}+23z^{2}a^{-4}-9a^{-4}+z^{9}a^{-3}+7z^{7}a^{-3}-26z^{5}a^{-3}+20z^{3}a^{-3}-9za^{-3}+5a^{-3}z^{-1}+5z^{8}a^{-2}-11z^{6}a^{-2}-9z^{4}a^{-2}+28z^{2}a^{-2}-14a^{-2}+z^{9}a^{-1}+az^{7}-6az^{5}-12z^{5}a^{-1}+13az^{3}+24z^{3}a^{-1}-12az-20za^{-1}+4az^{-1}+8a^{-1}z^{-1}+z^{8}-2z^{6}-5z^{4}+14z^{2}-8$ (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		\

-4

-3

-2

-1

0

1

2

3

4

5

6

χ

16

1

14

2

-2

12

4

1

3

10

5

2

-3

8

4

0

6

5

-1

4

3

4

-1

2

4

7

3

0

1

2

-1

-2

4

-4

1

0

-6

1

Integral Khovanov Homology

(db, data source)

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