L10a154

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,8,15,7 X_20,15,17,16 X_18,11,19,12 X_12,17,13,18 X_16,19,5,20 X_8,14,9,13 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -9, 2, -10}, {6, -5, 7, -4}, {9, -1, 3, -8, 10, -2, 5, -6, 8, -3, 4, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 - w u 3 + 3 u 3 + 4 v u 2 -2 v w u 2 + 4 w u 2 -5 u 2 -4 v u + 5 v w u -4 w u + 2 u + v -3 v w + w$ (db)
Jones polynomial	$q -3 + 7 q -1 -11 q -2 + 13 q -3 -13 q -4 + 13 q -5 -9 q -6 + 7 q -7 -2 q -8 + q -9$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$a 10 z -2 -2 a 8 z -2 -4 a 8 + 6 z 2 a 6 + a 6 z -2 + 6 a 6 -3 z 4 a 4 -5 z 2 a 4 -4 a 4 - z 4 a 2 + 2 z 2 a 2 + 2 a 2 + z 2$ (db)
Kauffman polynomial	$z 6 a 10 -4 z 4 a 10 + 6 z 2 a 10 + a 10 z -2 -4 a 10 + 2 z 7 a 9 -4 z 5 a 9 + 4 z a 9 -2 a 9 z -1 + 3 z 8 a 8 -5 z 6 a 8 - z 4 a 8 + 5 z 2 a 8 + 2 a 8 z -2 -5 a 8 + z 9 a 7 + 9 z 7 a 7 -29 z 5 a 7 + 22 z 3 a 7 -4 z a 7 -2 a 7 z -1 + 8 z 8 a 6 -11 z 6 a 6 -5 z 4 a 6 + 6 z 2 a 6 + a 6 z -2 -2 a 6 + z 9 a 5 + 15 z 7 a 5 -41 z 5 a 5 + 36 z 3 a 5 -12 z a 5 + 5 z 8 a 4 + z 6 a 4 -16 z 4 a 4 + 14 z 2 a 4 -2 a 4 + 8 z 7 a 3 -13 z 5 a 3 + 12 z 3 a 3 -4 z a 3 + 6 z 6 a 2 -7 z 4 a 2 + 6 z 2 a 2 -2 a 2 + 3 z 5 a -2 z 3 a + z 4 - z 2$ (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 =

-2 is the signature of L10a154. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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