L11n120

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,3,15,4 X_9,16,10,17 X_11,21,12,20 X_21,9,22,8 X_7,19,8,18 X_19,13,20,12 X_15,10,16,11 X_17,5,18,22 X₂₅₃₆ X_4,13,1,14
Gauss code	{1, -10, 2, -11}, {10, -1, -6, 5, -3, 8, -4, 7, 11, -2, -8, 3, -9, 6, -7, 4, -5, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$u 5 - v u 4 -3 u 4 + 2 v u 3 + 2 u 2 -3 v u - u + v$ (db)
Jones polynomial	$q^{9/2}-2 q^{7/2}+2 q^{5/2}-q^{3/2}-\frac{2}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z a 5 + a 5 z -1 -2 z 3 a 3 -5 z a 3 -2 a 3 z -1 + z 5 a + 5 z 3 a + 7 z a + 3 a z -1 - z 5 a -1 -5 z 3 a -1 -7 z a -1 -3 a -1 z -1 + z 3 a -3 + 2 z a -3 + a -3 z -1$ (db)
Kauffman polynomial	$- a 3 z 9 - a z 9 -2 a 4 z 8 -3 a 2 z 8 - z 8 a -2 -2 z 8 - a 5 z 7 + 3 a 3 z 7 + 4 a z 7 -2 z 7 a -1 -2 z 7 a -3 + 10 a 4 z 6 + 18 a 2 z 6 + 4 z 6 a -2 - z 6 a -4 + 13 z 6 + 5 a 5 z 5 + 6 a 3 z 5 + 6 a z 5 + 14 z 5 a -1 + 9 z 5 a -3 -12 a 4 z 4 -27 a 2 z 4 + z 4 a -2 + 4 z 4 a -4 -18 z 4 -7 a 5 z 3 -16 a 3 z 3 -23 a z 3 -22 z 3 a -1 -8 z 3 a -3 + 4 a 4 z 2 + 13 a 2 z 2 -6 z 2 a -2 -3 z 2 a -4 + 6 z 2 + 4 a 5 z + 10 a 3 z + 16 a z + 13 z a -1 + 3 z a -3 -2 a 2 + 2 a -2 + a -4 - a 5 z -1 -2 a 3 z -1 -3 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 =

1 is the signature of L11n120. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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