L11a110

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,4,15,3 X_16,8,17,7 X_18,10,19,9 X_20,12,21,11 X_22,14,5,13 X_8,18,9,17 X_10,20,11,19 X_12,22,13,21 X₂₅₃₆ X_4,16,1,15
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -7, 4, -8, 5, -9, 6, -2, 11, -3, 7, -4, 8, -5, 9, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 7 + u 7 + v u 6 - u 6 - v u 5 + u 5 + v u 4 - u 4 - v u 3 + u 3 + v u 2 - u 2 - v u + u + v -1$ (db)
Jones polynomial	$q 25 / 2 -2 q 23 / 2 + 3 q 21 / 2 -3 q 19 / 2 + 4 q 17 / 2 -4 q 15 / 2 + 4 q 13 / 2 -4 q 11 / 2 + 2 q 9 / 2 -3 q 7 / 2 + q 5 / 2 - q 3 / 2$ (db)
Signature	7 (db)
HOMFLY-PT polynomial	$- z 9 a -7 + z 7 a -5 -8 z 7 a -7 + z 7 a -9 + 7 z 5 a -5 -23 z 5 a -7 + 6 z 5 a -9 + 16 z 3 a -5 -31 z 3 a -7 + 11 z 3 a -9 + 14 z a -5 -22 z a -7 + 8 z a -9 + 4 a -5 z -1 -7 a -7 z -1 + 3 a -9 z -1$ (db)
Kauffman polynomial	$- z 10 a -6 - z 10 a -8 - z 9 a -5 -4 z 9 a -7 -3 z 9 a -9 + 6 z 8 a -6 + 3 z 8 a -8 -3 z 8 a -10 + 8 z 7 a -5 + 28 z 7 a -7 + 17 z 7 a -9 -3 z 7 a -11 -8 z 6 a -6 + 7 z 6 a -8 + 12 z 6 a -10 -3 z 6 a -12 -23 z 5 a -5 -66 z 5 a -7 -31 z 5 a -9 + 9 z 5 a -11 -3 z 5 a -13 -8 z 4 a -6 -27 z 4 a -8 -10 z 4 a -10 + 6 z 4 a -12 -3 z 4 a -14 + 30 z 3 a -5 + 65 z 3 a -7 + 25 z 3 a -9 -4 z 3 a -11 + 4 z 3 a -13 -2 z 3 a -15 + 19 z 2 a -6 + 23 z 2 a -8 + 3 z 2 a -14 - z 2 a -16 -18 z a -5 -30 z a -7 -12 z a -9 -7 a -6 -7 a -8 - a -14 + 4 a -5 z -1 + 7 a -7 z -1 + 3 a -9 z -1$ (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 =

7 is the signature of L11a110. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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