L11n250

(Knotscape image)

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

Planar diagram presentation	X_12,1,13,2 X_9,19,10,18 X_14,6,15,5 X_6,12,7,11 X_22,15,11,16 X_20,8,21,7 X₃₉₄₈ X_16,21,17,22 X_4,18,5,17 X_10,13,1,14 X_19,3,20,2
Gauss code	{1, 11, -7, -9, 3, -4, 6, 7, -2, -10}, {4, -1, 10, -3, 5, -8, 9, 2, -11, -6, 8, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + 3 v 2 u 3 -2 v u 3 + v 3 u 2 -4 v 2 u 2 + 2 v u 2 + 2 v 2 u -4 v u + u -2 v 2 + 3 v -1$ (db)
Jones polynomial	$q^{13/2}-4 q^{11/2}+6 q^{9/2}-8 q^{7/2}+8 q^{5/2}-9 q^{3/2}+7 \sqrt{q}-\frac{5}{\sqrt{q}}+\frac{3}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$z 7 a -3 -2 z 5 a -1 + 5 z 5 a -3 - z 5 a -5 + a z 3 -7 z 3 a -1 + 9 z 3 a -3 -4 z 3 a -5 + 2 a z -5 z a -1 + 8 z a -3 -4 z a -5 + z a -7 + a -3 z -1 - a -5 z -1$ (db)
Kauffman polynomial	$-2 z 9 a -1 -2 z 9 a -3 -8 z 8 a -2 -5 z 8 a -4 -3 z 8 - a z 7 + 4 z 7 a -1 -5 z 7 a -5 + 30 z 6 a -2 + 15 z 6 a -4 -2 z 6 a -6 + 13 z 6 + 4 a z 5 + 7 z 5 a -1 + 17 z 5 a -3 + 14 z 5 a -5 -29 z 4 a -2 -12 z 4 a -4 + z 4 a -6 -16 z 4 -5 a z 3 -13 z 3 a -1 -18 z 3 a -3 -14 z 3 a -5 -4 z 3 a -7 + 8 z 2 a -2 + 3 z 2 a -4 - z 2 a -6 - z 2 a -8 + 5 z 2 + 2 a z + 4 z a -1 + 7 z a -3 + 6 z a -5 + z a -7 + a -4 - a -3 z -1 - a -5 z -1$ (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 =

3 is the signature of L11n250. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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