L10a118

L10a117

L10a119

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L10a118 at Knotilus!

Rich Schwartz' "25" [1]

Two interlaced pentagons.

Two hollow interlaced pentagrams.

Link Presentations

[edit Notes on L10a118's Link Presentations]

Planar diagram presentation	X12,1,13,2 X2,13,3,14 X14,3,15,4 X16,5,17,6 X18,7,19,8 X20,9,11,10 X10,11,1,12 X4,15,5,16 X6,17,7,18 X8,19,9,20
Gauss code	{1, -2, 3, -8, 4, -9, 5, -10, 6, -7}, {7, -1, 2, -3, 8, -4, 9, -5, 10, -6}

A Braid Representative
A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...)	${\frac {-t(1)^{4}t(2)^{4}-t(1)^{3}t(2)^{3}-t(1)^{2}t(2)^{2}-t(1)t(2)-1}{t(1)^{2}t(2)^{2}}}$ (db)
Jones polynomial	$-{\frac {1}{q^{9/2}}}-{\frac {1}{q^{29/2}}}+{\frac {1}{q^{27/2}}}-{\frac {1}{q^{25/2}}}+{\frac {1}{q^{23/2}}}-{\frac {1}{q^{21/2}}}+{\frac {1}{q^{19/2}}}-{\frac {1}{q^{17/2}}}+{\frac {1}{q^{15/2}}}-{\frac {1}{q^{13/2}}}$ (db)
Signature	-9 (db)
HOMFLY-PT polynomial	$a^{11}z^{7}+7a^{11}z^{5}+15a^{11}z^{3}+10a^{11}z+a^{11}z^{-1}-a^{9}z^{9}-9a^{9}z^{7}-28a^{9}z^{5}-35a^{9}z^{3}-15a^{9}z-a^{9}z^{-1}$ (db)
Kauffman polynomial	$a^{19}z+a^{18}z^{2}+a^{17}z^{3}-a^{17}z+a^{16}z^{4}-2a^{16}z^{2}+a^{15}z^{5}-3a^{15}z^{3}+a^{15}z+a^{14}z^{6}-4a^{14}z^{4}+3a^{14}z^{2}+a^{13}z^{7}-5a^{13}z^{5}+6a^{13}z^{3}-a^{13}z+a^{12}z^{8}-6a^{12}z^{6}+10a^{12}z^{4}-4a^{12}z^{2}+a^{11}z^{9}-8a^{11}z^{7}+22a^{11}z^{5}-25a^{11}z^{3}+11a^{11}z-a^{11}z^{-1}+a^{10}z^{8}-7a^{10}z^{6}+15a^{10}z^{4}-10a^{10}z^{2}+a^{10}+a^{9}z^{9}-9a^{9}z^{7}+28a^{9}z^{5}-35a^{9}z^{3}+15a^{9}z-a^{9}z^{-1}$ (db)

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$).

\   r    \    j   \ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 χ -8                     1 1 -10                     1 1 -12                 1     1 -14                       0 -16             1 1       0 -18                       0 -20         1 1           0 -22                       0 -24     1 1               0 -26                       0 -28 1 1                   0 -30 1                     1

Integral Khovanov Homology (db, data source)

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

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). Back to the top.

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