L11a16

(Knotscape image)

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

Visit L11a16's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_4,17,1,18 X_14,6,15,5 X₈₄₉₃ X_18,10,19,9 X_20,12,21,11 X_22,14,5,13 X_10,20,11,19 X_12,22,13,21 X_2,16,3,15
Gauss code	{1, -11, 5, -3}, {4, -1, 2, -5, 6, -9, 7, -10, 8, -4, 11, -2, 3, -6, 9, -7, 10, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 7 + u 7 + 2 v u 6 -2 u 6 -2 v u 5 + 2 u 5 + 2 v u 4 -2 u 4 -2 v u 3 + 2 u 3 + 2 v u 2 -2 u 2 -2 v u + 2 u + v -1$ (db)
Jones polynomial	$-q^{21/2}+3 q^{19/2}-4 q^{17/2}+6 q^{15/2}-7 q^{13/2}+8 q^{11/2}-8 q^{9/2}+6 q^{7/2}-6 q^{5/2}+3 q^{3/2}-3 \sqrt{q}+\frac{1}{\sqrt{q}}$ (db)
Signature	5 (db)
HOMFLY-PT polynomial	$z 9 a -5 - z 7 a -3 + 7 z 7 a -5 - z 7 a -7 -5 z 5 a -3 + 16 z 5 a -5 -5 z 5 a -7 -5 z 3 a -3 + 12 z 3 a -5 -6 z 3 a -7 + 3 z a -3 -3 z a -5 + 3 a -3 z -1 -5 a -5 z -1 + 2 a -7 z -1$ (db)
Kauffman polynomial	$-2 z 10 a -4 -2 z 10 a -6 -3 z 9 a -3 -7 z 9 a -5 -4 z 9 a -7 - z 8 a -2 + 9 z 8 a -4 + 6 z 8 a -6 -4 z 8 a -8 + 18 z 7 a -3 + 38 z 7 a -5 + 16 z 7 a -7 -4 z 7 a -9 + 5 z 6 a -2 -8 z 6 a -4 + z 6 a -6 + 10 z 6 a -8 -4 z 6 a -10 -33 z 5 a -3 -63 z 5 a -5 -20 z 5 a -7 + 6 z 5 a -9 -4 z 5 a -11 -6 z 4 a -2 -2 z 4 a -4 -6 z 4 a -6 -4 z 4 a -8 + 3 z 4 a -10 -3 z 4 a -12 + 19 z 3 a -3 + 35 z 3 a -5 + 12 z 3 a -7 + 3 z 3 a -11 - z 3 a -13 + z 2 a -2 -3 z 2 a -4 -4 z 2 a -6 + 2 z 2 a -10 + 2 z 2 a -12 + 2 z a -3 + z a -5 - z a -7 + 5 a -4 + 5 a -6 - a -10 -3 a -3 z -1 -5 a -5 z -1 -2 a -7 z -1$ (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 =

5 is the signature of L11a16. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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