L11n102

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_3,13,4,12 X_7,16,8,17 X_17,22,18,5 X_13,18,14,19 X_21,14,22,15 X_9,20,10,21 X_15,8,16,9 X_19,10,20,11 X₂₅₃₆ X_11,1,12,4
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 $u$ , $v$ , $w$ , ...)	$-3 v u 3 + 3 u 3 + 7 v u 2 -7 u 2 -7 v u + 7 u + 3 v -3$ (db)
Jones polynomial	$-\sqrt{q}+\frac{3}{\sqrt{q}}-\frac{7}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{14}{q^{7/2}}+\frac{13}{q^{9/2}}-\frac{13}{q^{11/2}}+\frac{10}{q^{13/2}}-\frac{6}{q^{15/2}}+\frac{3}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 9 z -1 -2 z 3 a 7 - z a 7 + a 7 z -1 + 2 z 5 a 5 + 5 z 3 a 5 + 5 z a 5 + 2 a 5 z -1 + z 5 a 3 -3 z a 3 -2 a 3 z -1 - z 3 a - z a$ (db)
Kauffman polynomial	$-6 z 4 a 10 + 11 z 2 a 10 -4 a 10 -3 z 7 a 9 + 3 z 5 a 9 - z 3 a 9 + 2 z a 9 + a 9 z -1 -5 z 8 a 8 + 13 z 6 a 8 -24 z 4 a 8 + 25 z 2 a 8 -9 a 8 -2 z 9 a 7 -5 z 7 a 7 + 20 z 5 a 7 -25 z 3 a 7 + 9 z a 7 + a 7 z -1 -10 z 8 a 6 + 23 z 6 a 6 -24 z 4 a 6 + 12 z 2 a 6 -4 a 6 -2 z 9 a 5 -7 z 7 a 5 + 27 z 5 a 5 -33 z 3 a 5 + 15 z a 5 -2 a 5 z -1 -5 z 8 a 4 + 7 z 6 a 4 - z 4 a 4 -3 z 2 a 4 + 2 a 4 -5 z 7 a 3 + 9 z 5 a 3 -7 z 3 a 3 + 7 z a 3 -2 a 3 z -1 -3 z 6 a 2 + 5 z 4 a 2 - z 2 a 2 - z 5 a + 2 z 3 a - z a$ (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 L11n102. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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