L11a154

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 4 -2 v 2 u 3 + 6 v u 3 -3 u 3 + 4 v 2 u 2 -9 v u 2 + 4 u 2 -3 v 2 u + 6 v u -2 u -2 v$ (db)
Jones polynomial	$q^{9/2}-3 q^{7/2}+6 q^{5/2}-9 q^{3/2}+12 \sqrt{q}-\frac{14}{\sqrt{q}}+\frac{13}{q^{3/2}}-\frac{12}{q^{5/2}}+\frac{8}{q^{7/2}}-\frac{5}{q^{9/2}}+\frac{2}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 5 + 2 z a 5 + a 5 z -1 - z 5 a 3 -2 z 3 a 3 -2 z a 3 -2 z 5 a -5 z 3 a -5 z a -2 a z -1 - z 5 a -1 - z 3 a -1 + z a -1 + a -1 z -1 + z 3 a -3 + z a -3$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -3 a 3 z 9 -6 a z 9 -3 z 9 a -1 -3 a 4 z 8 -4 a 2 z 8 -4 z 8 a -2 -5 z 8 -3 a 5 z 7 + 7 a 3 z 7 + 18 a z 7 + 5 z 7 a -1 -3 z 7 a -3 -2 a 6 z 6 + 4 a 4 z 6 + 17 a 2 z 6 + 11 z 6 a -2 - z 6 a -4 + 23 z 6 - a 7 z 5 + 6 a 5 z 5 -12 a 3 z 5 -27 a z 5 + z 5 a -1 + 9 z 5 a -3 + 4 a 6 z 4 - a 4 z 4 -28 a 2 z 4 -8 z 4 a -2 + 3 z 4 a -4 -34 z 4 + 3 a 7 z 3 -5 a 5 z 3 + 7 a 3 z 3 + 21 a z 3 -6 z 3 a -3 - a 6 z 2 -2 a 4 z 2 + 15 a 2 z 2 + 5 z 2 a -2 -2 z 2 a -4 + 23 z 2 -2 a 7 z + 4 a 5 z - a 3 z -10 a z -2 z a -1 + z a -3 + a 4 -3 a 2 -2 a -2 -5- a 5 z -1 + 2 a z -1 + a -1 z -1$ (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 L11a154. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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