L11n194

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_16,6,17,5 X_9,20,10,21 X_21,10,22,11 X_18,16,19,15 X_14,20,15,19 X_2,11,3,12 X_12,3,13,4 X₄₇₅₈ X_22,14,7,13 X_6,18,1,17
Gauss code	{1, -7, 8, -9, 2, -11}, {9, -1, -3, 4, 7, -8, 10, -6, 5, -2, 11, -5, 6, 3, -4, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v 2 u 2 + 4 v u 2 - u 2 + 4 v 2 u -9 v u + 4 u - v 2 + 4 v -3$ (db)
Jones polynomial	$2 q^{5/2}-5 q^{3/2}+7 \sqrt{q}-\frac{11}{\sqrt{q}}+\frac{11}{q^{3/2}}-\frac{11}{q^{5/2}}+\frac{9}{q^{7/2}}-\frac{6}{q^{9/2}}+\frac{3}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 5 + z a 5 - z 5 a 3 - z 3 a 3 + z a 3 + a 3 z -1 -2 z 5 a -6 z 3 a -6 z a - a z -1 + 2 z 3 a -1 + 3 z a -1$ (db)
Kauffman polynomial	$- a 3 z 9 - a z 9 -3 a 4 z 8 -5 a 2 z 8 -2 z 8 -4 a 5 z 7 -5 a 3 z 7 -2 a z 7 - z 7 a -1 -3 a 6 z 6 + a 4 z 6 + 6 a 2 z 6 + 2 z 6 - a 7 z 5 + 6 a 5 z 5 + 8 a 3 z 5 -2 a z 5 -3 z 5 a -1 + 6 a 6 z 4 + 4 a 4 z 4 -4 a 2 z 4 -3 z 4 a -2 -5 z 4 + 2 a 7 z 3 - a 5 z 3 + 11 a z 3 + 8 z 3 a -1 -3 a 6 z 2 - a 4 z 2 + 3 a 2 z 2 + 4 z 2 a -2 + 5 z 2 - a 7 z -3 a 3 z -9 a z -5 z a -1 - a 2 + a 3 z -1 + a z -1$ (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 L11n194. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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