L11a250

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_2,11,3,12 X_12,3,13,4 X_14,6,15,5 X_22,18,9,17 X_4,19,5,20 X_6,22,7,21 X_16,7,17,8 X_8,9,1,10 X_18,14,19,13 X_20,15,21,16
Gauss code	{1, -2, 3, -6, 4, -7, 8, -9}, {9, -1, 2, -3, 10, -4, 11, -8, 5, -10, 6, -11, 7, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 5 + v 2 u 5 + 3 v 3 u 4 -4 v 2 u 4 + v u 4 -3 v 3 u 3 + 8 v 2 u 3 -5 v u 3 + u 3 + v 3 u 2 -5 v 2 u 2 + 8 v u 2 -3 u 2 + v 2 u -4 v u + 3 u + v -1$ (db)
Jones polynomial	$-q^{5/2}+4 q^{3/2}-7 \sqrt{q}+\frac{10}{\sqrt{q}}-\frac{15}{q^{3/2}}+\frac{16}{q^{5/2}}-\frac{17}{q^{7/2}}+\frac{15}{q^{9/2}}-\frac{11}{q^{11/2}}+\frac{7}{q^{13/2}}-\frac{4}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$a 3 z 9 - a 5 z 7 + 6 a 3 z 7 - a z 7 -4 a 5 z 5 + 11 a 3 z 5 -4 a z 5 -3 a 5 z 3 + 4 a 3 z 3 -3 a z 3 + 2 a 5 z -5 a 3 z + a z + a 5 z -1 - a 3 z -1$ (db)
Kauffman polynomial	$- z 4 a 10 -4 z 5 a 9 + 3 z 3 a 9 -7 z 6 a 8 + 7 z 4 a 8 - z 2 a 8 -8 z 7 a 7 + 7 z 5 a 7 + 3 z 3 a 7 -2 z a 7 -8 z 8 a 6 + 10 z 6 a 6 + z 4 a 6 -3 z 2 a 6 -7 z 9 a 5 + 15 z 7 a 5 -13 z 5 a 5 + 7 z 3 a 5 + z a 5 - a 5 z -1 -3 z 10 a 4 - z 8 a 4 + 21 z 6 a 4 -21 z 4 a 4 + 2 z 2 a 4 + a 4 -13 z 9 a 3 + 48 z 7 a 3 -54 z 5 a 3 + 17 z 3 a 3 + 4 z a 3 - a 3 z -1 -3 z 10 a 2 + 3 z 8 a 2 + 19 z 6 a 2 -27 z 4 a 2 + 6 z 2 a 2 -6 z 9 a + 24 z 7 a -27 z 5 a + 9 z 3 a + z a -4 z 8 + 15 z 6 -13 z 4 + 2 z 2 - z 7 a -1 + 3 z 5 a -1 - z 3 a -1$ (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 =

-3 is the signature of L11a250. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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