L10n14

(Knotscape image)

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

Visit L10n14's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_18,7,19,8 X_4,19,1,20 X_9,14,10,15 X₈₄₉₃ X_5,13,6,12 X_13,5,14,20 X_11,16,12,17 X_15,10,16,11 X_2,18,3,17
Gauss code	{1, -10, 5, -3}, {-6, -1, 2, -5, -4, 9, -8, 6, -7, 4, -9, 8, 10, -2, 3, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{(u-1) (v-1)}{\sqrt{u} \sqrt{v}}$ (db)
Jones polynomial	$-q^{5/2}+q^{3/2}-\sqrt{q}-\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{2}{q^{5/2}}+\frac{2}{q^{7/2}}-\frac{2}{q^{9/2}}+\frac{2}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 5 + 2 z a 5 + a 5 z -1 - z 5 a 3 -5 z 3 a 3 -8 z a 3 -3 a 3 z -1 + z 5 a + 6 z 3 a + 9 z a + 4 a z -1 - z 3 a -1 -3 z a -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 8 - z 8 - a 5 z 7 -2 a 3 z 7 -2 a z 7 - z 7 a -1 -2 a 6 z 6 -2 a 4 z 6 + 6 a 2 z 6 + 6 z 6 - a 7 z 5 + 3 a 5 z 5 + 13 a 3 z 5 + 15 a z 5 + 6 z 5 a -1 + 7 a 6 z 4 + 9 a 4 z 4 -6 a 2 z 4 -8 z 4 + 3 a 7 z 3 - a 5 z 3 -24 a 3 z 3 -30 a z 3 -10 z 3 a -1 -4 a 6 z 2 -10 a 4 z 2 -5 a 2 z 2 + z 2 - a 7 z + 2 a 5 z + 15 a 3 z + 19 a z + 7 z a -1 + a 6 + 3 a 4 + 3 a 2 + 2- a 5 z -1 -3 a 3 z -1 -4 a z -1 -2 a -1 z -1$ (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 L10n14. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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