L11a201

L11a200

L11a202

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a201 at Knotilus!

Link Presentations

[edit Notes on L11a201's Link Presentations]

Planar diagram presentation	X8192 X2,9,3,10 X10,3,11,4 X16,5,17,6 X22,18,7,17 X18,12,19,11 X12,22,13,21 X20,14,21,13 X14,20,15,19 X6718 X4,15,5,16
Gauss code	{1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, 6, -7, 8, -9, 11, -4, 5, -6, 9, -8, 7, -5}

A Braid Representative
A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...)	$-{\frac {2t(1)^{2}t(2)^{4}-5t(1)^{2}t(2)^{3}+4t(1)t(2)^{3}+4t(1)^{2}t(2)^{2}-7t(1)t(2)^{2}+4t(2)^{2}+4t(1)t(2)-5t(2)+2}{t(1)t(2)^{2}}}$ (db)
Jones polynomial	$q^{7/2}-2q^{5/2}+4q^{3/2}-7{\sqrt {q}}+{\frac {9}{\sqrt {q}}}-{\frac {11}{q^{3/2}}}+{\frac {11}{q^{5/2}}}-{\frac {11}{q^{7/2}}}+{\frac {8}{q^{9/2}}}-{\frac {6}{q^{11/2}}}+{\frac {3}{q^{13/2}}}-{\frac {1}{q^{15/2}}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$-a^{3}z^{7}-az^{7}+a^{5}z^{5}-4a^{3}z^{5}-5az^{5}+z^{5}a^{-1}+3a^{5}z^{3}-4a^{3}z^{3}-9az^{3}+4z^{3}a^{-1}+2a^{5}z-a^{3}z-8az+4za^{-1}+a^{5}z^{-1}-2az^{-1}+a^{-1}z^{-1}$ (db)
Kauffman polynomial	$a^{9}z^{3}+3a^{8}z^{4}+6a^{7}z^{5}-5a^{7}z^{3}+2a^{7}z+8a^{6}z^{6}-10a^{6}z^{4}+2a^{6}z^{2}+9a^{5}z^{7}-18a^{5}z^{5}+10a^{5}z^{3}-5a^{5}z+a^{5}z^{-1}+7a^{4}z^{8}-14a^{4}z^{6}+a^{4}z^{4}+3a^{4}z^{2}-a^{4}+4a^{3}z^{9}-6a^{3}z^{7}-9a^{3}z^{5}+9a^{3}z^{3}-a^{3}z+a^{2}z^{10}+6a^{2}z^{8}+z^{8}a^{-2}-34a^{2}z^{6}-6z^{6}a^{-2}+41a^{2}z^{4}+12z^{4}a^{-2}-16a^{2}z^{2}-9z^{2}a^{-2}+3a^{2}+2a^{-2}+6az^{9}+2z^{9}a^{-1}-26az^{7}-11z^{7}a^{-1}+35az^{5}+20z^{5}a^{-1}-21az^{3}-14z^{3}a^{-1}+10az+4za^{-1}-2az^{-1}-a^{-1}z^{-1}+z^{10}-18z^{6}+39z^{4}-26z^{2}+5$ (db)

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$).

\   r    \    j   \ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 χ 8                       1 -1 6                     1   1 4                   3 1   -2 2                 4 1     3 0               5 3       -2 -2             6 4         2 -4           6 6           0 -6         5 5             0 -8       3 6               3 -10     3 5                 -2 -12     3                   3 -14 1 3                     -2 -16 1                       1

Integral Khovanov Homology (db, data source)

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

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top.

L11a200 L11a202