L11n179

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_3,10,4,11 X_16,7,17,8 X_20,10,21,9 X_22,15,7,16 X_14,6,15,5 X_18,14,19,13 X_12,20,13,19 X_11,4,12,5 X_6,18,1,17 X_2,21,3,22
Gauss code	{1, -11, -2, 9, 6, -10}, {3, -1, 4, 2, -9, -8, 7, -6, 5, -3, 10, -7, 8, -4, 11, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 4 + u 4 - v 2 u 3 + 4 v u 3 -2 u 3 + 2 v 2 u 2 -7 v u 2 + 2 u 2 -2 v 2 u + 4 v u - u + v 2 - v$ (db)
Jones polynomial	$q^{5/2}-4 q^{3/2}+6 \sqrt{q}-\frac{9}{\sqrt{q}}+\frac{10}{q^{3/2}}-\frac{10}{q^{5/2}}+\frac{8}{q^{7/2}}-\frac{6}{q^{9/2}}+\frac{3}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 5 + z a 5 + a 5 z -1 - z 5 a 3 -2 z 3 a 3 -3 z a 3 -2 a 3 z -1 - z 5 a - z 3 a + z a + 2 a z -1 + z 3 a -1 - a -1 z -1$ (db)
Kauffman polynomial	$- a 3 z 9 - a z 9 -4 a 4 z 8 -5 a 2 z 8 - z 8 -5 a 5 z 7 -5 a 3 z 7 -3 a 6 z 6 + 9 a 4 z 6 + 12 a 2 z 6 - a 7 z 5 + 13 a 5 z 5 + 18 a 3 z 5 -4 z 5 a -1 + 6 a 6 z 4 -8 a 4 z 4 -15 a 2 z 4 - z 4 a -2 -2 z 4 + 2 a 7 z 3 -11 a 5 z 3 -23 a 3 z 3 -5 a z 3 + 5 z 3 a -1 - a 6 z 2 + 3 a 4 z 2 + 6 a 2 z 2 + z 2 a -2 + 3 z 2 + 5 a 5 z + 11 a 3 z + 7 a z + z a -1 - a 2 - a 5 z -1 -2 a 3 z -1 -2 a z -1 - a -1 z -1$ (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 L11n179. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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