L11n107

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_3,13,4,12 X_13,19,14,18 X_17,11,18,10 X_21,9,22,8 X_7,17,8,16 X_9,21,10,20 X_15,5,16,22 X_19,15,20,14 X₂₅₃₆ X_11,1,12,4
Gauss code	{1, -10, -2, 11}, {10, -1, -6, 5, -7, 4, -11, 2, -3, 9, -8, 6, -4, 3, -9, 7, -5, 8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v u 3 + 3 u 3 + 7 v u 2 -7 u 2 -7 v u + 7 u + 3 v -3$ (db)
Jones polynomial	$q 21 / 2 -3 q 19 / 2 + 7 q 17 / 2 -10 q 15 / 2 + 13 q 13 / 2 -14 q 11 / 2 + 12 q 9 / 2 -11 q 7 / 2 + 6 q 5 / 2 -3 q 3 / 2$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$-2 z 5 a -5 - z 5 a -7 + 3 z 3 a -3 -5 z 3 a -5 - z 3 a -7 + z 3 a -9 + 5 z a -3 -5 z a -5 - z a -7 + z a -9 + 2 a -3 z -1 -2 a -5 z -1 - a -7 z -1 + a -9 z -1$ (db)
Kauffman polynomial	$-2 z 9 a -7 -2 z 9 a -9 -6 z 8 a -6 -10 z 8 a -8 -4 z 8 a -10 -7 z 7 a -5 -8 z 7 a -7 -4 z 7 a -9 -3 z 7 a -11 -3 z 6 a -4 + 9 z 6 a -6 + 21 z 6 a -8 + 8 z 6 a -10 - z 6 a -12 + 14 z 5 a -5 + 25 z 5 a -7 + 19 z 5 a -9 + 8 z 5 a -11 -7 z 4 a -6 -11 z 4 a -8 - z 4 a -10 + 3 z 4 a -12 -6 z 3 a -3 -19 z 3 a -5 -19 z 3 a -7 -12 z 3 a -9 -6 z 3 a -11 -3 z 2 a -4 + 2 z 2 a -6 + 6 z 2 a -8 -2 z 2 a -10 -3 z 2 a -12 + 7 z a -3 + 10 z a -5 + 4 z a -7 + 2 z a -9 + z a -11 + 3 a -4 -3 a -8 + a -12 -2 a -3 z -1 -2 a -5 z -1 + a -7 z -1 + a -9 z -1$ (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 L11n107. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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