L11n200

L11n199

L11n201

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11n200 at Knotilus!

Link Presentations

[edit Notes on L11n200's Link Presentations]

Planar diagram presentation	X10,1,11,2 X12,3,13,4 X5,14,6,15 X16,7,17,8 X20,15,21,16 X13,18,14,19 X6,22,7,21 X22,18,9,17 X19,5,20,4 X2,9,3,10 X8,11,1,12
Gauss code	{1, -10, 2, 9, -3, -7, 4, -11}, {10, -1, 11, -2, -6, 3, 5, -4, 8, 6, -9, -5, 7, -8}

A Braid Representative
A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...)	$-{\frac {(t(1)+t(2))(t(2)t(1)-t(1)+1)(t(1)t(2)-t(2)+1)}{t(1)^{3/2}t(2)^{3/2}}}$ (db)
Jones polynomial	$-{\frac {6}{q^{9/2}}}+{\frac {5}{q^{7/2}}}-{\frac {6}{q^{5/2}}}+{\frac {4}{q^{3/2}}}-{\frac {1}{q^{17/2}}}+{\frac {2}{q^{15/2}}}-{\frac {3}{q^{13/2}}}+{\frac {5}{q^{11/2}}}+{\sqrt {q}}-{\frac {3}{\sqrt {q}}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z^{3}a^{7}+2za^{7}-z^{5}a^{5}-3z^{3}a^{5}-2za^{5}+a^{5}z^{-1}-z^{5}a^{3}-3z^{3}a^{3}-3za^{3}-a^{3}z^{-1}+z^{3}a+za$ (db)
Kauffman polynomial	$-z^{7}a^{9}+5z^{5}a^{9}-7z^{3}a^{9}+2za^{9}-2z^{8}a^{8}+10z^{6}a^{8}-15z^{4}a^{8}+7z^{2}a^{8}-z^{9}a^{7}+2z^{7}a^{7}+4z^{5}a^{7}-6z^{3}a^{7}-4z^{8}a^{6}+16z^{6}a^{6}-18z^{4}a^{6}+8z^{2}a^{6}-z^{9}a^{5}+z^{7}a^{5}+3z^{5}a^{5}+z^{3}a^{5}-za^{5}-a^{5}z^{-1}-2z^{8}a^{4}+5z^{6}a^{4}-3z^{4}a^{4}+z^{2}a^{4}+a^{4}-2z^{7}a^{3}+4z^{5}a^{3}-3z^{3}a^{3}+2za^{3}-a^{3}z^{-1}-z^{6}a^{2}-z^{2}a^{2}-3z^{3}a+za-z^{2}$ (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   \ -8 -7 -6 -5 -4 -3 -2 -1 0 1 χ 2                   1 -1 0                 2   2 -2               3 2   -1 -4             3 1     2 -6           2 3       1 -8         4 3         1 -10       2 3           1 -12     1 3             -2 -14   1 2               1 -16   1                 -1 -18 1                   1

Integral Khovanov Homology (db, data source)

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

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.

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