L11n60

(Knotscape image)

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

Visit L11n60's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,8,15,7 X_11,19,12,18 X_22,19,5,20 X_20,15,21,16 X_16,21,17,22 X_17,13,18,12 X_8,14,9,13 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -9, 11, -2, -4, 8, 9, -3, 6, -7, -8, 4, 5, -6, 7, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 5 - v u 4 + 3 u 4 + 4 v u 3 -6 u 3 -6 v u 2 + 4 u 2 + 3 v u - u - v$ (db)
Jones polynomial	$-q^{3/2}+4 \sqrt{q}-\frac{7}{\sqrt{q}}+\frac{9}{q^{3/2}}-\frac{11}{q^{5/2}}+\frac{9}{q^{7/2}}-\frac{9}{q^{9/2}}+\frac{6}{q^{11/2}}-\frac{3}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 7 - a 7 z -1 + 3 z 3 a 5 + 6 z a 5 + 4 a 5 z -1 -2 z 5 a 3 -7 z 3 a 3 -10 z a 3 -4 a 3 z -1 + 3 z 3 a + 4 z a + a z -1 - z a -1$ (db)
Kauffman polynomial	$- a 5 z 9 - a 3 z 9 -3 a 6 z 8 -6 a 4 z 8 -3 a 2 z 8 -3 a 7 z 7 -7 a 5 z 7 -6 a 3 z 7 -2 a z 7 - a 8 z 6 + 4 a 6 z 6 + 11 a 4 z 6 + 6 a 2 z 6 + 9 a 7 z 5 + 29 a 5 z 5 + 23 a 3 z 5 + 3 a z 5 + 3 a 8 z 4 + 9 a 6 z 4 + 4 a 4 z 4 -6 a 2 z 4 -4 z 4 -8 a 7 z 3 -29 a 5 z 3 -28 a 3 z 3 -8 a z 3 - z 3 a -1 -3 a 8 z 2 -11 a 6 z 2 -14 a 4 z 2 -4 a 2 z 2 + 2 z 2 + 4 a 7 z + 15 a 5 z + 14 a 3 z + 4 a z + z a -1 + a 8 + 4 a 6 + 7 a 4 + 4 a 2 + 1- a 7 z -1 -4 a 5 z -1 -4 a 3 z -1 - a z -1$ (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 =

-1 is the signature of L11n60. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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