L10a101

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L10a101 at Knotilus!
	[edit L10a101 Quick Notes] Contains two L4a1 configurations.

[edit L10a101 Further Notes and Views]

As a Celtic (or pseudo-Celtic) linear decorative knot

(multicolored)

Mongolian ornament

Rotated knotwork cross with four L10a101 sub-configurations

Link Presentations

[edit Notes on L10a101's Link Presentations]

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

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

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {(t(1)+t(2))\left(2t(2)t(1)^{2}-t(1)^{2}+2t(2)^{2}t(1)-4t(2)t(1)+2t(1)-t(2)^{2}+2t(2)\right)}{t(1)^{3/2}t(2)^{3/2}}}$ (db)
Jones polynomial	$-{\frac {1}{q^{3/2}}}+{\frac {3}{q^{5/2}}}-{\frac {6}{q^{7/2}}}+{\frac {7}{q^{9/2}}}-{\frac {9}{q^{11/2}}}+{\frac {9}{q^{13/2}}}-{\frac {8}{q^{15/2}}}+{\frac {6}{q^{17/2}}}-{\frac {4}{q^{19/2}}}+{\frac {2}{q^{21/2}}}-{\frac {1}{q^{23/2}}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$za^{11}-z^{3}a^{9}+za^{9}+a^{9}z^{-1}-3z^{3}a^{7}-3za^{7}-a^{7}z^{-1}-3z^{3}a^{5}-3za^{5}-z^{3}a^{3}$ (db)
Kauffman polynomial	$a^{13}z^{7}-5a^{13}z^{5}+8a^{13}z^{3}-4a^{13}z+2a^{12}z^{8}-9a^{12}z^{6}+12a^{12}z^{4}-4a^{12}z^{2}+a^{11}z^{9}-11a^{11}z^{5}+15a^{11}z^{3}-3a^{11}z+5a^{10}z^{8}-15a^{10}z^{6}+9a^{10}z^{4}+a^{10}z^{2}+a^{9}z^{9}+5a^{9}z^{7}-21a^{9}z^{5}+18a^{9}z^{3}-7a^{9}z+a^{9}z^{-1}+3a^{8}z^{8}+a^{8}z^{6}-15a^{8}z^{4}+8a^{8}z^{2}-a^{8}+6a^{7}z^{7}-9a^{7}z^{5}+4a^{7}z^{3}-5a^{7}z+a^{7}z^{-1}+7a^{6}z^{6}-9a^{6}z^{4}+3a^{6}z^{2}+6a^{5}z^{5}-6a^{5}z^{3}+3a^{5}z+3a^{4}z^{4}+a^{3}z^{3}$ (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

-2

1

-4

3

1

-2

-6

3

-8

4

3

-1

-10

5

3

2

-12

4

0

-14

4

5

-1

-16

2

4

2

-18

2

4

-2

-20

1

3

2

-22

1

-1

-24

1

Integral Khovanov Homology

(db, data source)

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