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

Visit L11a273 at Knotilus!

Link Presentations

[edit Notes on L11a273's Link Presentations]

Planar diagram presentation X10,1,11,2 X2,11,3,12 X12,3,13,4 X14,5,15,6 X6,9,7,10 X18,7,19,8 X22,19,9,20 X20,15,21,16 X16,21,17,22 X8,17,1,18 X4,13,5,14
Gauss code {1, -2, 3, -11, 4, -5, 6, -10}, {5, -1, 2, -3, 11, -4, 8, -9, 10, -6, 7, -8, 9, -7}
A Braid Representative
A Morse Link Presentation L11a273 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{-2 u^3 v^4+2 u^3 v^3-u^3 v^2-u^2 v^5+3 u^2 v^4-5 u^2 v^3+3 u^2 v^2-u^2 v-u v^4+3 u v^3-5 u v^2+3 u v-u-v^3+2 v^2-2 v}{u^{3/2} v^{5/2}} (db)
Jones polynomial -\frac{1}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{5}{q^{11/2}}+\frac{6}{q^{13/2}}-\frac{9}{q^{15/2}}+\frac{11}{q^{17/2}}-\frac{11}{q^{19/2}}+\frac{10}{q^{21/2}}-\frac{8}{q^{23/2}}+\frac{5}{q^{25/2}}-\frac{3}{q^{27/2}}+\frac{1}{q^{29/2}} (db)
Signature -7 (db)
HOMFLY-PT polynomial a^{13} \left(-z^3\right)-3 a^{13} z-a^{13} z^{-1} +3 a^{11} z^5+13 a^{11} z^3+14 a^{11} z+3 a^{11} z^{-1} -2 a^9 z^7-11 a^9 z^5-19 a^9 z^3-12 a^9 z-2 a^9 z^{-1} -a^7 z^7-5 a^7 z^5-7 a^7 z^3-3 a^7 z (db)
Kauffman polynomial -z^4 a^{18}+z^2 a^{18}-3 z^5 a^{17}+4 z^3 a^{17}-z a^{17}-4 z^6 a^{16}+4 z^4 a^{16}-4 z^7 a^{15}+3 z^5 a^{15}+2 z^3 a^{15}-2 z a^{15}-4 z^8 a^{14}+7 z^6 a^{14}-7 z^4 a^{14}+4 z^2 a^{14}-a^{14}-3 z^9 a^{13}+6 z^7 a^{13}-5 z^5 a^{13}+3 z^3 a^{13}-3 z a^{13}+a^{13} z^{-1} -z^{10} a^{12}-4 z^8 a^{12}+25 z^6 a^{12}-40 z^4 a^{12}+24 z^2 a^{12}-3 a^{12}-6 z^9 a^{11}+25 z^7 a^{11}-39 z^5 a^{11}+35 z^3 a^{11}-18 z a^{11}+3 a^{11} z^{-1} -z^{10} a^{10}-2 z^8 a^{10}+22 z^6 a^{10}-35 z^4 a^{10}+20 z^2 a^{10}-3 a^{10}-3 z^9 a^9+14 z^7 a^9-23 z^5 a^9+23 z^3 a^9-13 z a^9+2 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      53    -2
-18     66     0
-20    45      1
-22   46       -2
-24  25        3
-26 13         -2
-28 2          2
-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}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-9 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-8 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{4}
r=-7 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=-6 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=-5 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-4 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6} {\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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