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	$z^3 a^7+2 z a^7-z^5 a^5-3 z^3 a^5-2 z a^5+a^5 z^{-1} -z^5 a^3-3 z^3 a^3-3 z a^3-a^3 z^{-1} +z^3 a+z a$ (db)
Kauffman polynomial	$-z^7 a^9+5 z^5 a^9-7 z^3 a^9+2 z a^9-2 z^8 a^8+10 z^6 a^8-15 z^4 a^8+7 z^2 a^8-z^9 a^7+2 z^7 a^7+4 z^5 a^7-6 z^3 a^7-4 z^8 a^6+16 z^6 a^6-18 z^4 a^6+8 z^2 a^6-z^9 a^5+z^7 a^5+3 z^5 a^5+z^3 a^5-z a^5-a^5 z^{-1} -2 z^8 a^4+5 z^6 a^4-3 z^4 a^4+z^2 a^4+a^4-2 z^7 a^3+4 z^5 a^3-3 z^3 a^3+2 z a^3-a^3 z^{-1} -z^6 a^2-z^2 a^2-3 z^3 a+z a-z^2$ (db)

Khovanov Homology

The coefficients of the monomials $t^rq^j$ 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)

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

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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