L10n79

(Knotscape image)

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

Visit L10n79's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_5,14,6,15 X₈₄₉₃ X_2,16,3,15 X_16,7,17,8 X_9,18,10,19 X_11,20,12,13 X_13,12,14,5 X_4,17,1,18 X_19,10,20,11
Gauss code	{1, -4, 3, -9}, {-2, -1, 5, -3, -6, 10, -7, 8}, {-8, 2, 4, -5, 9, 6, -10, 7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-\frac{(u-1) (v-1) (w-1) (v w+1)}{\sqrt{u} v w}$ (db)
Jones polynomial	$2 q -2 -2 q -3 + 5 q -4 -5 q -5 + 6 q -6 -5 q -7 + 4 q -8 -2 q -9 + q -10$ (db)
Signature	-4 (db)
HOMFLY-PT polynomial	$z 4 a 8 + 3 z 2 a 8 + a 8 z -2 + 3 a 8 - z 6 a 6 -5 z 4 a 6 -10 z 2 a 6 -2 a 6 z -2 -9 a 6 + 2 z 4 a 4 + 7 z 2 a 4 + a 4 z -2 + 6 a 4$ (db)
Kauffman polynomial	$a 12 z 4 -2 a 12 z 2 + a 12 + 2 a 11 z 5 -3 a 11 z 3 + 2 a 10 z 6 - a 10 z 4 -2 a 10 z 2 + 2 a 9 z 7 -3 a 9 z 5 + 3 a 9 z 3 + a 8 z 8 - a 8 z 6 + 3 a 8 z 4 -3 a 8 z 2 - a 8 z -2 + 3 a 8 + 3 a 7 z 7 -8 a 7 z 5 + 13 a 7 z 3 -9 a 7 z + 2 a 7 z -1 + a 6 z 8 -3 a 6 z 6 + 8 a 6 z 4 -12 a 6 z 2 -2 a 6 z -2 + 9 a 6 + a 5 z 7 -3 a 5 z 5 + 7 a 5 z 3 -9 a 5 z + 2 a 5 z -1 + 3 a 4 z 4 -9 a 4 z 2 - a 4 z -2 + 6 a 4$ (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 =

-4 is the signature of L10n79. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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