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

Visit L11a201 at Knotilus!

Link Presentations

[edit Notes on L11a201's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X16,5,17,6 X22,18,7,17 X18,12,19,11 X12,22,13,21 X20,14,21,13 X14,20,15,19 X6718 X4,15,5,16
Gauss code {1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, 6, -7, 8, -9, 11, -4, 5, -6, 9, -8, 7, -5}
A Braid Representative
A Morse Link Presentation L11a201 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{2 t(1)^2 t(2)^4-5 t(1)^2 t(2)^3+4 t(1) t(2)^3+4 t(1)^2 t(2)^2-7 t(1) t(2)^2+4 t(2)^2+4 t(1) t(2)-5 t(2)+2}{t(1) t(2)^2} (db)
Jones polynomial q^{7/2}-2 q^{5/2}+4 q^{3/2}-7 \sqrt{q}+\frac{9}{\sqrt{q}}-\frac{11}{q^{3/2}}+\frac{11}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{8}{q^{9/2}}-\frac{6}{q^{11/2}}+\frac{3}{q^{13/2}}-\frac{1}{q^{15/2}} (db)
Signature -3 (db)
HOMFLY-PT polynomial -a^3 z^7-a z^7+a^5 z^5-4 a^3 z^5-5 a z^5+z^5 a^{-1} +3 a^5 z^3-4 a^3 z^3-9 a z^3+4 z^3 a^{-1} +2 a^5 z-a^3 z-8 a z+4 z a^{-1} +a^5 z^{-1} -2 a z^{-1} + a^{-1} z^{-1} (db)
Kauffman polynomial a^9 z^3+3 a^8 z^4+6 a^7 z^5-5 a^7 z^3+2 a^7 z+8 a^6 z^6-10 a^6 z^4+2 a^6 z^2+9 a^5 z^7-18 a^5 z^5+10 a^5 z^3-5 a^5 z+a^5 z^{-1} +7 a^4 z^8-14 a^4 z^6+a^4 z^4+3 a^4 z^2-a^4+4 a^3 z^9-6 a^3 z^7-9 a^3 z^5+9 a^3 z^3-a^3 z+a^2 z^{10}+6 a^2 z^8+z^8 a^{-2} -34 a^2 z^6-6 z^6 a^{-2} +41 a^2 z^4+12 z^4 a^{-2} -16 a^2 z^2-9 z^2 a^{-2} +3 a^2+2 a^{-2} +6 a z^9+2 z^9 a^{-1} -26 a z^7-11 z^7 a^{-1} +35 a z^5+20 z^5 a^{-1} -21 a z^3-14 z^3 a^{-1} +10 a z+4 z a^{-1} -2 a z^{-1} - a^{-1} z^{-1} +z^{10}-18 z^6+39 z^4-26 z^2+5 (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           1-1
6          1 1
4         31 -2
2        41  3
0       53   -2
-2      64    2
-4     66     0
-6    55      0
-8   36       3
-10  35        -2
-12  3         3
-1413          -2
-161           1
Integral Khovanov Homology

(db, data source)

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