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

Visit L11a487 at Knotilus!

Link Presentations

[edit Notes on L11a487's Link Presentations]

Planar diagram presentation X6172 X14,7,15,8 X4,15,1,16 X22,10,19,9 X8493 X16,21,17,22 X18,11,5,12 X20,5,21,6 X10,17,11,18 X12,20,13,19 X2,14,3,13
Gauss code {1, -11, 5, -3}, {10, -8, 6, -4}, {8, -1, 2, -5, 4, -9, 7, -10, 11, -2, 3, -6, 9, -7}
A Braid Representative
A Morse Link Presentation L11a487 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{(t(1)-1) (t(2)-1) (t(3)-1)^3 \left(t(3)^2-t(3)+1\right)}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{5/2}} (db)
Jones polynomial q^3-5 q^2+12 q-18+28 q^{-1} -30 q^{-2} +32 q^{-3} -27 q^{-4} +20 q^{-5} -13 q^{-6} +5 q^{-7} - q^{-8} (db)
Signature -2 (db)
HOMFLY-PT polynomial -a^6 z^4-a^6 z^2-a^6 z^{-2} -a^6+2 a^4 z^6+5 a^4 z^4+4 a^4 z^2+4 a^4 z^{-2} +4 a^4-a^2 z^8-4 a^2 z^6-6 a^2 z^4-4 a^2 z^2-5 a^2 z^{-2} -5 a^2+z^6+2 z^4+z^2+2 z^{-2} +2 (db)
Kauffman polynomial a^9 z^5+5 a^8 z^6-2 a^8 z^4+13 a^7 z^7-16 a^7 z^5+7 a^7 z^3-3 a^7 z+a^7 z^{-1} +18 a^6 z^8-27 a^6 z^6+14 a^6 z^4-4 a^6 z^2-a^6 z^{-2} +a^6+13 a^5 z^9-4 a^5 z^7-23 a^5 z^5+18 a^5 z^3-10 a^5 z+5 a^5 z^{-1} +4 a^4 z^{10}+28 a^4 z^8-72 a^4 z^6+49 a^4 z^4-13 a^4 z^2-4 a^4 z^{-2} +4 a^4+24 a^3 z^9-38 a^3 z^7+3 a^3 z^5+14 a^3 z^3-12 a^3 z+9 a^3 z^{-1} +4 a^2 z^{10}+21 a^2 z^8-65 a^2 z^6+z^6 a^{-2} +51 a^2 z^4-z^4 a^{-2} -13 a^2 z^2-5 a^2 z^{-2} +5 a^2+11 a z^9-16 a z^7+5 z^7 a^{-1} +a z^5-8 z^5 a^{-1} +5 a z^3+2 z^3 a^{-1} -5 a z+5 a z^{-1} +11 z^8-24 z^6+17 z^4-4 z^2-2 z^{-2} +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).   
\ r
j \
7           11
5          4 -4
3         81 7
1        104  -6
-1       188   10
-3      1614    -2
-5     1614     2
-7    1116      5
-9   916       -7
-11  411        7
-13 19         -8
-15 4          4
-171           -1
Integral Khovanov Homology

(db, data source)

\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-3 i=-1
r=-7 {\mathbb Z}
r=-6 {\mathbb Z}^{4}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-5 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=-4 {\mathbb Z}^{11}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{9}
r=-3 {\mathbb Z}^{16}\oplus{\mathbb Z}_2^{11} {\mathbb Z}^{11}
r=-2 {\mathbb Z}^{16}\oplus{\mathbb Z}_2^{16} {\mathbb Z}^{16}
r=-1 {\mathbb Z}^{14}\oplus{\mathbb Z}_2^{16} {\mathbb Z}^{16}
r=0 {\mathbb Z}^{14}\oplus{\mathbb Z}_2^{14} {\mathbb Z}^{18}
r=1 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10} {\mathbb Z}^{10}
r=2 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{8}
r=3 {\mathbb Z}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=4 {\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

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See/edit the Link Page master template (intermediate).

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