L10a102

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L10a102 at Knotilus!
	[edit L10a102 Quick Notes]

[edit L10a102 Further Notes and Views]

Link Presentations

[edit Notes on L10a102's Link Presentations]

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

A Braid Representative

A Morse Link Presentation

Polynomial invariants

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

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

χ

-6

1

-8

1

0

-10

2

-12

2

1

-1

-14

4

2

-16

2

0

-18

4

0

-20

2

0

-22

2

4

-2

-24

1

3

2

-26

1

-1

-28

1

Integral Khovanov Homology

(db, data source)

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