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

Visit L9a33 at Knotilus!

L9a33 is 9^2_{24} in the Rolfsen table of links.

Symmetric form
Alternate symmetric version, with three lines touching at center
Alternate symmetric version, with three lines touching at circumference
Form made from 45-degree lines and circular arcs.
Depiction obtained by knotilus.
With an hypotrochoid [1].
Mexican book.

Link Presentations

[edit Notes on L9a33's Link Presentations]

Planar diagram presentation X8192 X12,3,13,4 X18,10,7,9 X10,14,11,13 X16,5,17,6 X14,18,15,17 X2738 X4,11,5,12 X6,15,1,16
Gauss code {1, -7, 2, -8, 5, -9}, {7, -1, 3, -4, 8, -2, 4, -6, 9, -5, 6, -3}
A Braid Representative
A Morse Link Presentation L9a33 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{u^2 v^2-3 u^2 v+3 u^2-3 u v^2+7 u v-3 u+3 v^2-3 v+1}{u v} (db)
Jones polynomial -\frac{6}{q^{9/2}}+\frac{7}{q^{7/2}}+q^{5/2}-\frac{9}{q^{5/2}}-4 q^{3/2}+\frac{10}{q^{3/2}}-\frac{1}{q^{13/2}}+\frac{2}{q^{11/2}}+6 \sqrt{q}-\frac{8}{\sqrt{q}} (db)
Signature -1 (db)
HOMFLY-PT polynomial a^7 z^{-1} -3 a^5 z-a^5 z^{-1} +3 a^3 z^3+3 a^3 z-a z^5-2 a z^3+z^3 a^{-1} -3 a z (db)
Kauffman polynomial -a^4 z^8-a^2 z^8-3 a^5 z^7-7 a^3 z^7-4 a z^7-2 a^6 z^6-7 a^4 z^6-11 a^2 z^6-6 z^6-a^7 z^5+5 a^5 z^5+9 a^3 z^5-a z^5-4 z^5 a^{-1} +3 a^6 z^4+18 a^4 z^4+24 a^2 z^4-z^4 a^{-2} +8 z^4+3 a^7 z^3-3 a^5 z^3-2 a^3 z^3+8 a z^3+4 z^3 a^{-1} -11 a^4 z^2-14 a^2 z^2-3 z^2-3 a^7 z+a^5 z+2 a^3 z-2 a z-a^6+a^7 z^{-1} +a^5 z^{-1} (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 \
6         1-1
4        3 3
2       31 -2
0      53  2
-2     64   -2
-4    34    -1
-6   46     2
-8  23      -1
-10  4       4
-1212        -1
-141         1
Integral Khovanov Homology

(db, data source)

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

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