L11n144

(Knotscape image)

See the full Thistlethwaite Link Table (up to 11 crossings).

Planar diagram presentation	X₈₁₉₂ X_11,19,12,18 X_3,10,4,11 X_2,17,3,18 X_12,5,13,6 X₆₇₁₈ X_16,10,17,9 X_20,16,21,15 X_22,14,7,13 X_14,22,15,21 X_19,4,20,5
Gauss code	{1, -4, -3, 11, 5, -6}, {6, -1, 7, 3, -2, -5, 9, -10, 8, -7, 4, 2, -11, -8, 10, -9}

A Braid Representative

A Morse Link Presentation

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

The coefficients of the monomials

t r q j

are shown, along with their alternating sums

χ

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j -2 r = s + 1

j -2 r = s -1

, where

s =

-1 is the signature of L11n144. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}$
$r = -4$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 0$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = 1$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$