L11a150

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_16,7,17,8 X_10,4,11,3 X_2,15,3,16 X_14,10,15,9 X_18,11,19,12 X_12,5,13,6 X_6,21,1,22 X_20,14,21,13 X_22,17,7,18 X_4,20,5,19
Gauss code	{1, -4, 3, -11, 7, -8}, {2, -1, 5, -3, 6, -7, 9, -5, 4, -2, 10, -6, 11, -9, 8, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 3 v u 4 - u 4 + 7 v 2 u 3 -12 v u 3 + 5 u 3 -9 v 2 u 2 + 19 v u 2 -9 u 2 + 5 v 2 u -12 v u + 7 u - v 2 + 3 v -2$ (db)
Jones polynomial	$-q^{7/2}+5 q^{5/2}-12 q^{3/2}+20 \sqrt{q}-\frac{28}{\sqrt{q}}+\frac{31}{q^{3/2}}-\frac{32}{q^{5/2}}+\frac{27}{q^{7/2}}-\frac{20}{q^{9/2}}+\frac{12}{q^{11/2}}-\frac{5}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a 3 z 7 + a z 7 - a 5 z 5 + 2 a 3 z 5 + 2 a z 5 - z 5 a -1 - a 5 z 3 + a 3 z 3 + a z 3 - z 3 a -1 - a z + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$-5 a 4 z 10 -5 a 2 z 10 -12 a 5 z 9 -26 a 3 z 9 -14 a z 9 -11 a 6 z 8 -16 a 4 z 8 -22 a 2 z 8 -17 z 8 -5 a 7 z 7 + 19 a 5 z 7 + 47 a 3 z 7 + 11 a z 7 -12 z 7 a -1 - a 8 z 6 + 22 a 6 z 6 + 53 a 4 z 6 + 59 a 2 z 6 -5 z 6 a -2 + 24 z 6 + 8 a 7 z 5 -4 a 5 z 5 -18 a 3 z 5 + 9 a z 5 + 14 z 5 a -1 - z 5 a -3 + a 8 z 4 -13 a 6 z 4 -36 a 4 z 4 -36 a 2 z 4 + 3 z 4 a -2 -11 z 4 -3 a 7 z 3 -2 a 5 z 3 -6 a z 3 -5 z 3 a -1 + 2 a 6 z 2 + 6 a 4 z 2 + 6 a 2 z 2 + 2 z 2 - a 3 z - a z - a 2 + a 3 z -1 + a z -1$ (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 L11a150. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -4$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -3$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = -2$	${\mathbb Z}^{17}\oplus{\mathbb Z}_2^{15}$	${\mathbb Z}^{16}$
$r = -1$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{16}$	${\mathbb Z}^{16}$
$r = 0$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{15}$	${\mathbb Z}^{16}$
$r = 1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$