L11a514

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 - v u 3 - v 2 w u 3 + 2 v w u 3 -2 v 2 u 2 - v 2 w 2 u 2 + 2 v w 2 u 2 + 3 v u 2 + 3 v 2 w u 2 -5 v w u 2 + 2 w u 2 - u 2 + v 2 w 2 u -3 v w 2 u + 2 w 2 u -2 v u -2 v 2 w u + 5 v w u -3 w u + u + v w 2 - w 2 -2 v w + w$ (db)
Jones polynomial	$- q 4 + 3 q 3 -5 q 2 + 10 q -12 + 15 q -1 -15 q -2 + 14 q -3 -10 q -4 + 7 q -5 -3 q -6 + q -7$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$z 2 a 6 + a 6 -2 z 4 a 4 -3 z 2 a 4 + a 4 z -2 + a 4 + z 6 a 2 + z 4 a 2 -4 z 2 a 2 -2 a 2 z -2 -6 a 2 + z 6 + 3 z 4 + 4 z 2 + z -2 + 4- z 4 a -2 -2 z 2 a -2$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 3 a 3 z 9 + 6 a z 9 + 3 z 9 a -1 + 6 a 4 z 8 + 8 a 2 z 8 + 3 z 8 a -2 + 5 z 8 + 7 a 5 z 7 + 6 a 3 z 7 -11 a z 7 -9 z 7 a -1 + z 7 a -3 + 6 a 6 z 6 -5 a 4 z 6 -24 a 2 z 6 -13 z 6 a -2 -26 z 6 + 3 a 7 z 5 -8 a 5 z 5 -25 a 3 z 5 -5 a z 5 + 5 z 5 a -1 -4 z 5 a -3 + a 8 z 4 -8 a 6 z 4 - a 4 z 4 + 23 a 2 z 4 + 18 z 4 a -2 + 33 z 4 -2 a 7 z 3 + 4 a 5 z 3 + 22 a 3 z 3 + 14 a z 3 + 2 z 3 a -1 + 4 z 3 a -3 - a 8 z 2 + 7 a 6 z 2 - a 4 z 2 -21 a 2 z 2 -8 z 2 a -2 -20 z 2 -9 a 3 z -9 a z -2 a 6 + 3 a 4 + 11 a 2 + 7 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

-2 is the signature of L11a514. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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