L10a118

(Knotscape image)

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

Rich Schwartz' "25" [1]

Two interlaced pentagons.

Two hollow interlaced pentagrams.

Planar diagram presentation	X_12,1,13,2 X_2,13,3,14 X_14,3,15,4 X_16,5,17,6 X_18,7,19,8 X_20,9,11,10 X_10,11,1,12 X_4,15,5,16 X_6,17,7,18 X_8,19,9,20
Gauss code	{1, -2, 3, -8, 4, -9, 5, -10, 6, -7}, {7, -1, 2, -3, 8, -4, 9, -5, 10, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{-u^4 v^4-u^3 v^3-u^2 v^2-u v-1}{u^2 v^2}$ (db)
Jones polynomial	$-\frac{1}{q^{9/2}}-\frac{1}{q^{13/2}}+\frac{1}{q^{15/2}}-\frac{1}{q^{17/2}}+\frac{1}{q^{19/2}}-\frac{1}{q^{21/2}}+\frac{1}{q^{23/2}}-\frac{1}{q^{25/2}}+\frac{1}{q^{27/2}}-\frac{1}{q^{29/2}}$ (db)
Signature	-9 (db)
HOMFLY-PT polynomial	$z 7 a 11 + 7 z 5 a 11 + 15 z 3 a 11 + 10 z a 11 + a 11 z -1 - z 9 a 9 -9 z 7 a 9 -28 z 5 a 9 -35 z 3 a 9 -15 z a 9 - a 9 z -1$ (db)
Kauffman polynomial	$- z a 19 - z 2 a 18 - z 3 a 17 + z a 17 - z 4 a 16 + 2 z 2 a 16 - z 5 a 15 + 3 z 3 a 15 - z a 15 - z 6 a 14 + 4 z 4 a 14 -3 z 2 a 14 - z 7 a 13 + 5 z 5 a 13 -6 z 3 a 13 + z a 13 - z 8 a 12 + 6 z 6 a 12 -10 z 4 a 12 + 4 z 2 a 12 - z 9 a 11 + 8 z 7 a 11 -22 z 5 a 11 + 25 z 3 a 11 -11 z a 11 + a 11 z -1 - z 8 a 10 + 7 z 6 a 10 -15 z 4 a 10 + 10 z 2 a 10 - a 10 - z 9 a 9 + 9 z 7 a 9 -28 z 5 a 9 + 35 z 3 a 9 -15 z a 9 + a 9 z -1$ (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 =

-9 is the signature of L10a118. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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