L11n104

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,3,13,4 X_7,16,8,17 X_22,18,5,17 X_18,14,19,13 X_21,14,22,15 X_9,20,10,21 X_15,8,16,9 X_19,10,20,11 X₂₅₃₆ X_4,11,1,12
Gauss code	{1, -10, 2, -11}, {10, -1, -3, 8, -7, 9, 11, -2, 5, 6, -8, 3, 4, -5, -9, 7, -6, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 + 2 u 3 + 6 v u 2 -6 u 2 -6 v u + 6 u + 2 v -1$ (db)
Jones polynomial	$-\sqrt{q}+\frac{4}{\sqrt{q}}-\frac{7}{q^{3/2}}+\frac{8}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{10}{q^{9/2}}-\frac{9}{q^{11/2}}+\frac{6}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 9 z -1 + 4 z a 7 + 3 a 7 z -1 -4 z 3 a 5 -6 z a 5 -2 a 5 z -1 + z 5 a 3 + z 3 a 3 - z 3 a$ (db)
Kauffman polynomial	$- z 4 a 10 + 2 z 2 a 10 - a 10 -3 z 5 a 9 + 4 z 3 a 9 - z a 9 + a 9 z -1 - z 8 a 8 + 2 z 6 a 8 -9 z 4 a 8 + 10 z 2 a 8 -3 a 8 - z 9 a 7 + z 7 a 7 -5 z 5 a 7 + 6 z 3 a 7 -7 z a 7 + 3 a 7 z -1 -5 z 8 a 6 + 12 z 6 a 6 -17 z 4 a 6 + 10 z 2 a 6 -3 a 6 - z 9 a 5 -5 z 7 a 5 + 12 z 5 a 5 -4 z 3 a 5 -6 z a 5 + 2 a 5 z -1 -4 z 8 a 4 + 6 z 6 a 4 -2 z 4 a 4 + 2 z 2 a 4 -6 z 7 a 3 + 13 z 5 a 3 -5 z 3 a 3 -4 z 6 a 2 + 7 z 4 a 2 - z 5 a + z 3 a$ (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 L11n104. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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