L11n106

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,3,13,4 X_7,16,8,17 X_17,22,18,5 X_13,18,14,19 X_9,21,10,20 X_19,14,20,15 X_21,9,22,8 X_15,10,16,11 X₂₅₃₆ X_4,11,1,12
Gauss code	{1, -10, 2, -11}, {10, -1, -3, 8, -6, 9, 11, -2, -5, 7, -9, 3, -4, 5, -7, 6, -8, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + 2 v u 4 + 2 u 4 + v u 3 -3 u 3 -3 v u 2 + u 2 + 2 v u + 2 u -1$ (db)
Jones polynomial	$-\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{1}{q^{5/2}}+\frac{1}{q^{9/2}}-\frac{3}{q^{11/2}}+\frac{2}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{3}{q^{17/2}}-\frac{2}{q^{19/2}}+\frac{1}{q^{21/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 11 z -1 + 4 z a 9 + 3 a 9 z -1 - z 5 a 7 -7 z 3 a 7 -9 z a 7 -3 a 7 z -1 + z 7 a 5 + 6 z 5 a 5 + 10 z 3 a 5 + 8 z a 5 + 2 a 5 z -1 - z 5 a 3 -5 z 3 a 3 -5 z a 3 - a 3 z -1$ (db)
Kauffman polynomial	$- z 6 a 12 + 4 z 4 a 12 -3 z 2 a 12 + a 12 -2 z 7 a 11 + 8 z 5 a 11 -6 z 3 a 11 + 3 z a 11 - a 11 z -1 -2 z 8 a 10 + 8 z 6 a 10 -4 z 4 a 10 -3 z 2 a 10 + 2 a 10 - z 9 a 9 + 3 z 7 a 9 + 5 z 5 a 9 -15 z 3 a 9 + 11 z a 9 -3 a 9 z -1 -3 z 8 a 8 + 17 z 6 a 8 -24 z 4 a 8 + 9 z 2 a 8 - z 9 a 7 + 4 z 7 a 7 + 5 z 5 a 7 -22 z 3 a 7 + 14 z a 7 -3 a 7 z -1 -2 z 8 a 6 + 14 z 6 a 6 -25 z 4 a 6 + 14 z 2 a 6 -2 a 6 -2 z 7 a 5 + 14 z 5 a 5 -23 z 3 a 5 + 12 z a 5 -2 a 5 z -1 - z 8 a 4 + 6 z 6 a 4 -9 z 4 a 4 + 5 z 2 a 4 - z 7 a 3 + 6 z 5 a 3 -10 z 3 a 3 + 6 z a 3 - a 3 z -1$ (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 =

-3 is the signature of L11n106. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -6$	$i = -4$	$i = -2$
$r = -9$		${\mathbb Z}$
$r = -8$		${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -7$		${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$		${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -5$	${\mathbb Z}$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -4$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -1$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = 0$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}^{2}$
$r = 1$	${\mathbb Z}$
$r = 2$	${\mathbb Z}_2$	${\mathbb Z}$