L11a501

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_14,5,15,6 X_10,3,11,4 X_4,13,5,14 X₂₇₃₈ X_6,9,1,10 X_18,12,19,11 X_12,18,7,17 X_20,16,21,15 X_22,20,13,19 X_16,22,17,21
Gauss code	{1, -5, 3, -4, 2, -6}, {5, -1, 6, -3, 7, -8}, {4, -2, 9, -11, 8, -7, 10, -9, 11, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 - v w 2 u 3 - v u 3 - v 2 w u 3 + 2 v w u 3 - w u 3 -2 v 2 u 2 + 3 v w 2 u 2 -2 w 2 u 2 + 3 v u 2 + 3 v 2 w u 2 -6 v w u 2 + 3 w u 2 + 2 v 2 u -3 v w 2 u + 2 w 2 u -3 v u -3 v 2 w u + 6 v w u -3 w u + v w 2 - w 2 + v + v 2 w -2 v w + w$ (db)
Jones polynomial	$- q 5 + 3 q 4 -7 q 3 + 12 q 2 -16 q + 19-18 q -1 + 17 q -2 -11 q -3 + 8 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- a 2 z 6 - z 6 + a 4 z 4 -3 a 2 z 4 + 2 z 4 a -2 - z 4 + 2 a 4 z 2 -7 a 2 z 2 + 3 z 2 a -2 - z 2 a -4 + 2 z 2 + 3 a 4 -9 a 2 + a -2 - a -4 + 6 + 2 a 4 z -2 -5 a 2 z -2 - a -2 z -2 + 4 z -2$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 4 a 3 z 9 + 7 a z 9 + 3 z 9 a -1 + 6 a 4 z 8 + 12 a 2 z 8 + 5 z 8 a -2 + 11 z 8 + 3 a 5 z 7 -2 a 3 z 7 -2 a z 7 + 8 z 7 a -1 + 5 z 7 a -3 + a 6 z 6 -19 a 4 z 6 -39 a 2 z 6 -2 z 6 a -2 + 3 z 6 a -4 -24 z 6 -7 a 5 z 5 -17 a 3 z 5 -29 a z 5 -27 z 5 a -1 -7 z 5 a -3 + z 5 a -5 -3 a 6 z 4 + 26 a 4 z 4 + 51 a 2 z 4 -6 z 4 a -2 -5 z 4 a -4 + 21 z 4 + 3 a 5 z 3 + 28 a 3 z 3 + 50 a z 3 + 31 z 3 a -1 + 4 z 3 a -3 -2 z 3 a -5 + 2 a 6 z 2 -23 a 4 z 2 -43 a 2 z 2 + 5 z 2 a -2 + 3 z 2 a -4 -16 z 2 -19 a 3 z -35 a z -19 z a -1 -2 z a -3 + z a -5 + 11 a 4 + 22 a 2 - a -4 + 13 + 5 a 3 z -1 + 9 a z -1 + 5 a -1 z -1 + a -3 z -1 -2 a 4 z -2 -5 a 2 z -2 - a -2 z -2 -4 z -2$ (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 =

0 is the signature of L11a501. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -6$	${\mathbb Z}$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{7}$
$r = -1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{10}$
$r = 1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 2$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 3$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$