L11a192

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,3,11,4 X_16,6,17,5 X_22,11,7,12 X_20,13,21,14 X_18,15,19,16 X_14,19,15,20 X_12,21,13,22 X_4,18,5,17 X₂₇₃₈ X_6,9,1,10
Gauss code	{1, -10, 2, -9, 3, -11}, {10, -1, 11, -2, 4, -8, 5, -7, 6, -3, 9, -6, 7, -5, 8, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v u 2 + 3 u 2 -3 v 2 u + 7 v u -3 u + 3 v 2 -3 v$ (db)
Jones polynomial	$-q^{3/2}+2 \sqrt{q}-\frac{4}{\sqrt{q}}+\frac{5}{q^{3/2}}-\frac{7}{q^{5/2}}+\frac{7}{q^{7/2}}-\frac{7}{q^{9/2}}+\frac{6}{q^{11/2}}-\frac{5}{q^{13/2}}+\frac{3}{q^{15/2}}-\frac{2}{q^{17/2}}+\frac{1}{q^{19/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 9 + z 3 a 7 + 2 z 3 a 5 + z a 5 + 2 z 3 a 3 + z a 3 + a 3 z -1 + z 3 a - z a - a z -1 - z a -1$ (db)
Kauffman polynomial	$- z 8 a 10 + 6 z 6 a 10 -11 z 4 a 10 + 6 z 2 a 10 -2 z 9 a 9 + 12 z 7 a 9 -23 z 5 a 9 + 16 z 3 a 9 -3 z a 9 - z 10 a 8 + 3 z 8 a 8 + 3 z 6 a 8 -11 z 4 a 8 + 4 z 2 a 8 -4 z 9 a 7 + 19 z 7 a 7 -26 z 5 a 7 + 12 z 3 a 7 -2 z a 7 - z 10 a 6 + z 8 a 6 + 7 z 6 a 6 -8 z 4 a 6 + z 2 a 6 -2 z 9 a 5 + 4 z 7 a 5 + 3 z 5 a 5 -4 z 3 a 5 + z a 5 -3 z 8 a 4 + 7 z 6 a 4 -4 z 4 a 4 + 3 z 2 a 4 -3 z 7 a 3 + 3 z 5 a 3 + 4 z 3 a 3 -4 z a 3 + a 3 z -1 -3 z 6 a 2 + 2 z 4 a 2 + z 2 a 2 - a 2 -3 z 5 a + 3 z 3 a -3 z a + a z -1 -2 z 4 + z 2 - z 3 a -1 + z a -1$ (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 L11a192. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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