Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)

# L10n100

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## Contents

 (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L10n100's page at Knotilus. Visit L10n100's page at the original Knot Atlas.

### Link Presentations

 Planar diagram presentation X6172 X3,11,4,10 X7,15,8,14 X13,5,14,8 X11,18,12,19 X20,16,17,15 X16,20,9,19 X17,12,18,13 X2536 X9,1,10,4 Gauss code {1, -9, -2, 10}, {9, -1, -3, 4}, {-8, 5, 7, -6}, {-10, 2, -5, 8, -4, 3, 6, -7}
A Braid Representative
A Morse Link Presentation

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{(u-1) (v-1) (w-1) (x-1)}{\sqrt{u} \sqrt{v} \sqrt{w} \sqrt{x}}$ (db) Jones polynomial $-2 q^{9/2}+3 q^{7/2}-7 q^{5/2}+4 q^{3/2}-7 \sqrt{q}+\frac{4}{\sqrt{q}}-\frac{4}{q^{3/2}}+\frac{1}{q^{5/2}}$ (db) Signature 1 (db) HOMFLY-PT polynomial $- a^{-5} z^{-3} - a^{-5} z^{-1} -z^3 a^{-3} +3 a^{-3} z^{-3} +z a^{-3} +4 a^{-3} z^{-1} +z^5 a^{-1} -a z^3+2 z^3 a^{-1} +a z^{-3} -3 a^{-1} z^{-3} -z a^{-1} +2 a z^{-1} -5 a^{-1} z^{-1}$ (db) Kauffman polynomial $-z^7 a^{-1} -z^7 a^{-3} -5 z^6 a^{-2} -z^6 a^{-4} -4 z^6-4 a z^5-6 z^5 a^{-1} -2 z^5 a^{-3} -a^2 z^4+6 z^4 a^{-2} +5 z^4+6 a z^3+10 z^3 a^{-1} +z^3 a^{-3} -3 z^3 a^{-5} -6 z^2 a^{-2} -5 z^2 a^{-4} -z^2+z a^{-1} +5 z a^{-3} +4 z a^{-5} +11 a^{-2} +6 a^{-4} +6-3 a z^{-1} -6 a^{-1} z^{-1} -6 a^{-3} z^{-1} -3 a^{-5} z^{-1} -6 a^{-2} z^{-2} -3 a^{-4} z^{-2} -3 z^{-2} +a z^{-3} +3 a^{-1} z^{-3} +3 a^{-3} z^{-3} + a^{-5} z^{-3}$ (db)

### Khovanov Homology

 The coefficients of the monomials $t^rq^j$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$1 is the signature of L10n100. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. Data:L10n100/KhovanovTable
Integral Khovanov Homology
 $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=0$ $i=2$ $r=-3$ ${\mathbb Z}$ $r=-2$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-1$ ${\mathbb Z}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=0$ ${\mathbb Z}^{6}\oplus{\mathbb Z}_2$ ${\mathbb Z}^{7}$ $r=1$ ${\mathbb Z}^{4}$ $r=2$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=3$ ${\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=4$ ${\mathbb Z}^{2}$ ${\mathbb Z}^{2}$

### 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).

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