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

Visit L11a33 at Knotilus!

Link Presentations

[edit Notes on L11a33's Link Presentations]

Planar diagram presentation X6172 X10,3,11,4 X18,11,19,12 X16,7,17,8 X8,17,9,18 X20,13,21,14 X22,15,5,16 X12,19,13,20 X14,21,15,22 X2536 X4,9,1,10
Gauss code {1, -10, 2, -11}, {10, -1, 4, -5, 11, -2, 3, -8, 6, -9, 7, -4, 5, -3, 8, -6, 9, -7}
A Braid Representative
A Morse Link Presentation L11a33 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{-2 u v^6+3 u v^5-3 u v^4+3 u v^3-3 u v^2+2 u v-u-v^7+2 v^6-3 v^5+3 v^4-3 v^3+3 v^2-2 v}{\sqrt{u} v^{7/2}} (db)
Jones polynomial \frac{2}{q^{9/2}}-\frac{1}{q^{7/2}}+\frac{1}{q^{29/2}}-\frac{2}{q^{27/2}}+\frac{5}{q^{25/2}}-\frac{7}{q^{23/2}}+\frac{9}{q^{21/2}}-\frac{11}{q^{19/2}}+\frac{10}{q^{17/2}}-\frac{9}{q^{15/2}}+\frac{6}{q^{13/2}}-\frac{5}{q^{11/2}} (db)
Signature -7 (db)
HOMFLY-PT polynomial -z^3 a^{13}-4 z a^{13}-3 a^{13} z^{-1} +3 z^5 a^{11}+14 z^3 a^{11}+18 z a^{11}+7 a^{11} z^{-1} -2 z^7 a^9-11 z^5 a^9-19 z^3 a^9-13 z a^9-4 a^9 z^{-1} -z^7 a^7-5 z^5 a^7-7 z^3 a^7-3 z a^7 (db)
Kauffman polynomial -z^4 a^{18}+2 z^2 a^{18}-a^{18}-2 z^5 a^{17}+2 z^3 a^{17}-3 z^6 a^{16}+3 z^4 a^{16}-z^2 a^{16}-3 z^7 a^{15}+2 z^5 a^{15}-3 z^8 a^{14}+4 z^6 a^{14}-3 z^4 a^{14}+z^2 a^{14}-3 z^9 a^{13}+9 z^7 a^{13}-17 z^5 a^{13}+20 z^3 a^{13}-12 z a^{13}+3 a^{13} z^{-1} -z^{10} a^{12}-3 z^8 a^{12}+22 z^6 a^{12}-39 z^4 a^{12}+29 z^2 a^{12}-7 a^{12}-6 z^9 a^{11}+27 z^7 a^{11}-49 z^5 a^{11}+53 z^3 a^{11}-31 z a^{11}+7 a^{11} z^{-1} -z^{10} a^{10}-2 z^8 a^{10}+23 z^6 a^{10}-39 z^4 a^{10}+26 z^2 a^{10}-7 a^{10}-3 z^9 a^9+14 z^7 a^9-23 z^5 a^9+24 z^3 a^9-16 z a^9+4 a^9 z^{-1} -2 z^8 a^8+8 z^6 a^8-7 z^4 a^8+z^2 a^8-z^7 a^7+5 z^5 a^7-7 z^3 a^7+3 z a^7 (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           11
-8          21-1
-10         3  3
-12        32  -1
-14       63   3
-16      54    -1
-18     65     1
-20    35      2
-22   46       -2
-24  13        2
-26 14         -3
-28 1          1
-301           -1
Integral Khovanov Homology

(db, data source)

\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-8 i=-6
r=-11 {\mathbb Z}
r=-10 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-9 {\mathbb Z}^{4}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-8 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=-7 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-6 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=-5 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-4 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{6}
r=-3 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-2 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-1 {\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=0 {\mathbb Z} {\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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