L11n273

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_16,7,17,8 X_8,15,5,16 X_11,19,12,18 X_17,9,18,22 X_21,13,22,12 X_13,21,14,20 X_19,15,20,14 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -4}, {11, -2, -5, 7, -8, 9, 4, -3, -6, 5, -9, 8, -7, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 + 2 w u 3 -2 u 3 -3 v u 2 -3 w u 2 + u 2 + 3 v u - v w u + 3 w u -2 v + 2 v w -2 w$ (db)
Jones polynomial	$-2 q 3 + 3 q 2 -6 q + 9-8 q -1 + 9 q -2 -6 q -3 + 6 q -4 -2 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 z -2 + a 6 -3 z 2 a 4 - a 4 z -2 -4 a 4 + 2 z 4 a 2 + 3 z 2 a 2 -2 a 2 z -2 - a 2 + 2 z 4 + 5 z 2 + 3 z -2 + 7-2 z 2 a -2 - a -2 z -2 -3 a -2$ (db)
Kauffman polynomial	$a 3 z 9 + a z 9 + 2 a 4 z 8 + 6 a 2 z 8 + 4 z 8 + 2 a 5 z 7 + 3 a 3 z 7 + 5 a z 7 + 4 z 7 a -1 + a 6 z 6 -2 a 4 z 6 -19 a 2 z 6 + z 6 a -2 -15 z 6 -5 a 5 z 5 -17 a 3 z 5 -29 a z 5 -17 z 5 a -1 -4 a 6 z 4 -8 a 4 z 4 + 19 a 2 z 4 + 23 z 4 + 18 a 3 z 3 + 50 a z 3 + 35 z 3 a -1 + 3 z 3 a -3 + 6 a 6 z 2 + 6 a 4 z 2 -8 a 2 z 2 - z 2 a -2 -9 z 2 + 4 a 5 z -10 a 3 z -34 a z -27 z a -1 -7 z a -3 -4 a 6 -3 a 4 + 4 a 2 + a -2 + 5-2 a 5 z -1 + 2 a 3 z -1 + 10 a z -1 + 8 a -1 z -1 + 2 a -3 z -1 + a 6 z -2 + a 4 z -2 -2 a 2 z -2 - a -2 z -2 -3 z -2$ (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 =

0 is the signature of L11n273. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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