L11a24

(Knotscape image)

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

Visit L11a24's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,8,15,7 X_18,11,19,12 X_22,19,5,20 X_20,15,21,16 X_16,21,17,22 X_12,17,13,18 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 $u$ , $v$ , $w$ , ...)	$\frac{3 u v^4-10 u v^3+12 u v^2-7 u v+u+v^5-7 v^4+12 v^3-10 v^2+3 v}{\sqrt{u} v^{5/2}}$ (db)
Jones polynomial	$-\sqrt{q}+\frac{3}{\sqrt{q}}-\frac{8}{q^{3/2}}+\frac{14}{q^{5/2}}-\frac{19}{q^{7/2}}+\frac{21}{q^{9/2}}-\frac{22}{q^{11/2}}+\frac{18}{q^{13/2}}-\frac{14}{q^{15/2}}+\frac{8}{q^{17/2}}-\frac{3}{q^{19/2}}+\frac{1}{q^{21/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 11 z -1 + 4 a 9 z + 3 a 9 z -1 -6 a 7 z 3 -9 a 7 z -3 a 7 z -1 + 3 a 5 z 5 + 7 a 5 z 3 + 7 a 5 z + 2 a 5 z -1 + a 3 z 5 - a 3 z 3 -3 a 3 z - a 3 z -1 - a z 3 - a z$ (db)
Kauffman polynomial	$- z 6 a 12 + 3 z 4 a 12 -3 z 2 a 12 + a 12 -3 z 7 a 11 + 7 z 5 a 11 -6 z 3 a 11 + 3 z a 11 - a 11 z -1 -5 z 8 a 10 + 9 z 6 a 10 -3 z 4 a 10 -2 z 2 a 10 + 2 a 10 -4 z 9 a 9 -2 z 7 a 9 + 21 z 5 a 9 -21 z 3 a 9 + 11 z a 9 -3 a 9 z -1 - z 10 a 8 -16 z 8 a 8 + 42 z 6 a 8 -34 z 4 a 8 + 12 z 2 a 8 -9 z 9 a 7 + 2 z 7 a 7 + 31 z 5 a 7 -36 z 3 a 7 + 15 z a 7 -3 a 7 z -1 - z 10 a 6 -19 z 8 a 6 + 48 z 6 a 6 -45 z 4 a 6 + 18 z 2 a 6 -2 a 6 -5 z 9 a 5 -5 z 7 a 5 + 27 z 5 a 5 -31 z 3 a 5 + 13 z a 5 -2 a 5 z -1 -8 z 8 a 4 + 13 z 6 a 4 -13 z 4 a 4 + 6 z 2 a 4 -6 z 7 a 3 + 9 z 5 a 3 -8 z 3 a 3 + 5 z a 3 - a 3 z -1 -3 z 6 a 2 + 4 z 4 a 2 - z 2 a 2 - z 5 a + 2 z 3 a - z a$ (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 =

-3 is the signature of L11a24. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -4$	$i = -2$
$r = -9$	${\mathbb Z}$
$r = -8$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -6$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -5$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -4$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{11}$
$r = -3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = -2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -1$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 0$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{6}$
$r = 1$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 2$	${\mathbb Z}_2$	${\mathbb Z}$