L10n106

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_5,12,6,13 X₃₈₄₉ X_15,2,16,3 X_16,7,17,8 X_9,11,10,14 X_13,15,14,20 X_19,5,20,10 X_11,18,12,19 X_4,17,1,18
Gauss code	{1, 4, -3, -10}, {-9, 2, -7, 6}, {-2, -1, 5, 3, -6, 8}, {-4, -5, 10, 9, -8, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 w u 2 - v w u 2 - v 2 w x u 2 + v w x u 2 - v u - v 2 w u + v w u + v x u + v 2 w x u - v w x u - x u + u + v - v x + x -1$ (db)
Jones polynomial	$q^{3/2}-3 \sqrt{q}+\frac{3}{\sqrt{q}}-\frac{6}{q^{3/2}}+\frac{4}{q^{5/2}}-\frac{7}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{4}{q^{11/2}}+\frac{1}{q^{13/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- z a 7 + a 7 z -3 + z 5 a 5 + 4 z 3 a 5 + 3 z a 5 -2 a 5 z -1 -3 a 5 z -3 - z 7 a 3 -5 z 5 a 3 -7 z 3 a 3 -2 z a 3 + 4 a 3 z -1 + 3 a 3 z -3 + z 5 a + 3 z 3 a -2 a z -1 - a z -3$ (db)
Kauffman polynomial	$- z 2 a 8 -4 z 3 a 7 + 3 z a 7 + 2 a 7 z -1 - a 7 z -3 -2 z 6 a 6 + 4 z 4 a 6 -3 z 2 a 6 + 3 a 6 z -2 -4 a 6 -4 z 7 a 5 + 16 z 5 a 5 -24 z 3 a 5 + 11 z a 5 + 3 a 5 z -1 -3 a 5 z -3 -2 z 8 a 4 + 4 z 6 a 4 + 3 z 4 a 4 -4 z 2 a 4 + 6 a 4 z -2 -7 a 4 -7 z 7 a 3 + 28 z 5 a 3 -32 z 3 a 3 + 11 z a 3 + 3 a 3 z -1 -3 a 3 z -3 -2 z 8 a 2 + 5 z 6 a 2 + 2 z 4 a 2 -3 z 2 a 2 + 3 a 2 z -2 -4 a 2 -3 z 7 a + 12 z 5 a -12 z 3 a + 3 z a + 2 a z -1 - a z -3 - z 6 + 3 z 4 - z 2$ (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 =

-3 is the signature of L10n106. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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