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

Visit L11a149 at Knotilus!

Link Presentations

[edit Notes on L11a149's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X14,17,15,18 X16,7,17,8 X22,15,7,16 X18,13,19,14 X6,20,1,19 X20,12,21,11 X12,6,13,5 X4,21,5,22
Gauss code {1, -2, 3, -11, 10, -8}, {5, -1, 2, -3, 9, -10, 7, -4, 6, -5, 4, -7, 8, -9, 11, -6}
A Braid Representative
A Morse Link Presentation L11a149 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{2 u^2 v^4-5 u^2 v^3+5 u^2 v^2-2 u^2 v-2 u v^4+8 u v^3-11 u v^2+8 u v-2 u-2 v^3+5 v^2-5 v+2}{u v^2} (db)
Jones polynomial \frac{19}{q^{9/2}}-\frac{19}{q^{7/2}}+\frac{15}{q^{5/2}}+q^{3/2}-\frac{12}{q^{3/2}}-\frac{1}{q^{19/2}}+\frac{4}{q^{17/2}}-\frac{8}{q^{15/2}}+\frac{13}{q^{13/2}}-\frac{17}{q^{11/2}}-3 \sqrt{q}+\frac{6}{\sqrt{q}} (db)
Signature -3 (db)
HOMFLY-PT polynomial a^7 z^5+2 a^7 z^3-a^7 z^{-1} -a^5 z^7-3 a^5 z^5-a^5 z^3+4 a^5 z+3 a^5 z^{-1} -a^3 z^7-4 a^3 z^5-7 a^3 z^3-7 a^3 z-2 a^3 z^{-1} +a z^5+3 a z^3+2 a z (db)
Kauffman polynomial a^{11} z^5-a^{11} z^3+4 a^{10} z^6-6 a^{10} z^4+a^{10} z^2+7 a^9 z^7-11 a^9 z^5+3 a^9 z^3+8 a^8 z^8-13 a^8 z^6+6 a^8 z^4-a^8+6 a^7 z^9-8 a^7 z^7+5 a^7 z^5-2 a^7 z^3+a^7 z^{-1} +2 a^6 z^{10}+7 a^6 z^8-21 a^6 z^6+18 a^6 z^4-3 a^6+10 a^5 z^9-24 a^5 z^7+24 a^5 z^5-6 a^5 z^3-5 a^5 z+3 a^5 z^{-1} +2 a^4 z^{10}+3 a^4 z^8-13 a^4 z^6+10 a^4 z^4+a^4 z^2-3 a^4+4 a^3 z^9-6 a^3 z^7-2 a^3 z^5+8 a^3 z^3-8 a^3 z+2 a^3 z^{-1} +4 a^2 z^8-8 a^2 z^6+a^2 z^4+2 a^2 z^2+3 a z^7-9 a z^5+8 a z^3-3 a z+z^6-3 z^4+2 z^2 (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 \
4           1-1
2          2 2
0         41 -3
-2        82  6
-4       85   -3
-6      117    4
-8     99     0
-10    810      -2
-12   59       4
-14  38        -5
-16 15         4
-18 3          -3
-201           1
Integral Khovanov Homology

(db, data source)

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

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

See/edit the Link_Splice_Base (expert).

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