L11a152

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L11a151.gif

L11a151

L11a153.gif

L11a153

Contents

L11a152.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a152 at Knotilus!


Link Presentations

[edit Notes on L11a152's Link Presentations]

Planar diagram presentation X8192 X10,3,11,4 X12,17,13,18 X14,5,15,6 X4,13,5,14 X18,11,19,12 X22,19,7,20 X20,15,21,16 X16,21,17,22 X2738 X6,9,1,10
Gauss code {1, -10, 2, -5, 4, -11}, {10, -1, 11, -2, 6, -3, 5, -4, 8, -9, 3, -6, 7, -8, 9, -7}
A Braid Representative
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A Morse Link Presentation L11a152 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{3 u^2 v^3-5 u^2 v^2+4 u^2 v-u^2+3 u v^4-8 u v^3+11 u v^2-8 u v+3 u-v^4+4 v^3-5 v^2+3 v}{u v^2} (db)
Jones polynomial -\frac{8}{q^{9/2}}+\frac{3}{q^{7/2}}-\frac{1}{q^{5/2}}+\frac{1}{q^{27/2}}-\frac{3}{q^{25/2}}+\frac{7}{q^{23/2}}-\frac{12}{q^{21/2}}+\frac{16}{q^{19/2}}-\frac{19}{q^{17/2}}+\frac{19}{q^{15/2}}-\frac{17}{q^{13/2}}+\frac{12}{q^{11/2}} (db)
Signature -5 (db)
HOMFLY-PT polynomial a^{13} (-z)-a^{13} z^{-1} +3 a^{11} z^3+5 a^{11} z+2 a^{11} z^{-1} -2 a^9 z^5-3 a^9 z^3-3 a^7 z^5-8 a^7 z^3-6 a^7 z-a^7 z^{-1} -a^5 z^5-2 a^5 z^3-a^5 z (db)
Kauffman polynomial a^{16} z^6-3 a^{16} z^4+2 a^{16} z^2+3 a^{15} z^7-8 a^{15} z^5+6 a^{15} z^3-2 a^{15} z+5 a^{14} z^8-13 a^{14} z^6+12 a^{14} z^4-7 a^{14} z^2+2 a^{14}+4 a^{13} z^9-4 a^{13} z^7-6 a^{13} z^5+7 a^{13} z^3-a^{13} z-a^{13} z^{-1} +a^{12} z^{10}+12 a^{12} z^8-38 a^{12} z^6+44 a^{12} z^4-25 a^{12} z^2+5 a^{12}+8 a^{11} z^9-10 a^{11} z^7-a^{11} z^3+6 a^{11} z-2 a^{11} z^{-1} +a^{10} z^{10}+13 a^{10} z^8-32 a^{10} z^6+30 a^{10} z^4-13 a^{10} z^2+3 a^{10}+4 a^9 z^9+3 a^9 z^7-14 a^9 z^5+11 a^9 z^3-3 a^9 z+6 a^8 z^8-5 a^8 z^6-3 a^8 z^4+4 a^8 z^2-a^8+6 a^7 z^7-11 a^7 z^5+11 a^7 z^3-7 a^7 z+a^7 z^{-1} +3 a^6 z^6-4 a^6 z^4+a^6 z^2+a^5 z^5-2 a^5 z^3+a^5 z (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 \
-11-10-9-8-7-6-5-4-3-2-10χ
-4           11
-6          31-2
-8         5  5
-10        73  -4
-12       105   5
-14      97    -2
-16     1010     0
-18    710      3
-20   59       -4
-22  27        5
-24 15         -4
-26 2          2
-281           -1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-6 i=-4
r=-11 {\mathbb Z}
r=-10 {\mathbb Z}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-9 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-8 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-7 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{7}
r=-6 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{10}
r=-5 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{9}
r=-4 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{10} {\mathbb Z}^{10}
r=-3 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{7}
r=-2 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-1 {\mathbb Z}_2^{3} {\mathbb Z}^{3}
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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L11a151.gif

L11a151

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L11a153