L11a100

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_18,9,19,10 X_20,11,21,12 X_8,17,9,18 X_10,19,11,20 X_4,21,1,22 X_14,6,15,5 X_12,4,13,3 X_22,14,5,13 X_2,16,3,15
Gauss code	{1, -11, 9, -7}, {8, -1, 2, -5, 3, -6, 4, -9, 10, -8, 11, -2, 5, -3, 6, -4, 7, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 7 + u 7 + 2 v u 6 -2 u 6 -3 v u 5 + 3 u 5 + 3 v u 4 -3 u 4 -3 v u 3 + 3 u 3 + 3 v u 2 -3 u 2 -2 v u + 2 u + v -1$ (db)
Jones polynomial	$-q^{5/2}+3 q^{3/2}-5 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{10}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{10}{q^{9/2}}-\frac{7}{q^{11/2}}+\frac{5}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$a 3 z 9 - a 5 z 7 + 7 a 3 z 7 - a z 7 -5 a 5 z 5 + 17 a 3 z 5 -5 a z 5 -7 a 5 z 3 + 17 a 3 z 3 -7 a z 3 -3 a 5 z + 7 a 3 z -4 a z - a 5 z -1 + 3 a 3 z -1 -2 a z -1$ (db)
Kauffman polynomial	$- z 4 a 10 + z 2 a 10 -3 z 5 a 9 + 4 z 3 a 9 -4 z 6 a 8 + 5 z 4 a 8 - z 2 a 8 -4 z 7 a 7 + 5 z 5 a 7 -2 z 3 a 7 -4 z 8 a 6 + 8 z 6 a 6 -7 z 4 a 6 + 2 z 2 a 6 - a 6 -4 z 9 a 5 + 14 z 7 a 5 -23 z 5 a 5 + 18 z 3 a 5 -6 z a 5 + a 5 z -1 -2 z 10 a 4 + 4 z 8 a 4 + 3 z 6 a 4 -11 z 4 a 4 + 8 z 2 a 4 -3 a 4 -8 z 9 a 3 + 38 z 7 a 3 -63 z 5 a 3 + 46 z 3 a 3 -13 z a 3 + 3 a 3 z -1 -2 z 10 a 2 + 5 z 8 a 2 + 4 z 6 a 2 -11 z 4 a 2 + 6 z 2 a 2 -3 a 2 -4 z 9 a + 19 z 7 a -28 z 5 a + 19 z 3 a -7 z a + 2 a z -1 -3 z 8 + 13 z 6 -13 z 4 + 2 z 2 - z 7 a -1 + 4 z 5 a -1 -3 z 3 a -1$ (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 L11a100. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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