L11n44

(Knotscape image)

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

Visit L11n44's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_4,17,1,18 X_5,14,6,15 X₃₈₄₉ X_9,18,10,19 X_11,20,12,21 X_13,22,14,5 X_19,10,20,11 X_21,12,22,13 X_15,2,16,3
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 $u$ , $v$ , $w$ , ...)	$- v u 7 -1$ (db)
Jones polynomial	$-\frac{1}{q^{9/2}}-\frac{1}{q^{13/2}}-\frac{1}{q^{17/2}}+\frac{1}{q^{27/2}}$ (db)
Signature	-9 (db)
HOMFLY-PT polynomial	$- z 3 a 13 -4 z a 13 -3 a 13 z -1 + z 7 a 11 + 8 z 5 a 11 + 21 z 3 a 11 + 21 z a 11 + 7 a 11 z -1 - z 9 a 9 -9 z 7 a 9 -28 z 5 a 9 -36 z 3 a 9 -19 z a 9 -4 a 9 z -1$ (db)
Kauffman polynomial	$- a 18 - z 5 a 13 + 6 z 3 a 13 -9 z a 13 + 3 a 13 z -1 - z 8 a 12 + 8 z 6 a 12 -21 z 4 a 12 + 21 z 2 a 12 -7 a 12 - z 9 a 11 + 9 z 7 a 11 -29 z 5 a 11 + 42 z 3 a 11 -28 z a 11 + 7 a 11 z -1 - z 8 a 10 + 8 z 6 a 10 -21 z 4 a 10 + 21 z 2 a 10 -7 a 10 - z 9 a 9 + 9 z 7 a 9 -28 z 5 a 9 + 36 z 3 a 9 -19 z a 9 + 4 a 9 z -1$ (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 =

-9 is the signature of L11n44. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -10$	$i = -8$	$i = -6$
$r = -9$	${\mathbb Z}$	${\mathbb Z}$
$r = -8$	${\mathbb Z}_2$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -7$	${\mathbb Z}$	${\mathbb Z}$
$r = -6$	${\mathbb Z}_2$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}_2$	${\mathbb Z}^{2}$	${\mathbb Z}$
$r = -3$	${\mathbb Z}$
$r = -2$	${\mathbb Z}_2$	${\mathbb Z}$
$r = -1$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$