© | Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table:

L11n148 L11n150

Knotscape

This page is passe. Go here instead! The 2-Component Link L11n149 Visit L11n149's page at Knotilus! Acknowledgement

DrawMorseLink

PD Presentation:

X8192 X9,19,10,18 X6718 X22,19,7,20 X12,5,13,6 X3,10,4,11 X4,15,5,16 X16,12,17,11 X20,13,21,14 X14,21,15,22 X17,2,18,3

Gauss Code:

{{1, 11, -6, -7, 5, -3}, {3, -1, -2, 6, 8, -5, 9, -10, 7, -8, -11, 2, 4, -9, 10, -4}}

Jones Polynomial:

q-21/2 - 3q-19/2 + 4q-17/2 - 6q-15/2 + 7q-13/2 - 7q-11/2 + 6q-9/2 - 5q-7/2 + 2q-5/2 - q-3/2

A2 (sl(3)) Invariant:

- q-32 + q-30 + 3q-24 + q-20 + 2q-14 + 2q-10 + q-8 - q-6 + q-4

HOMFLY-PT Polynomial:

- a3z - a3z3 - a5z-1 - 5a5z - 3a5z3 + a7z-1 + 4a7z + 3a7z3 + a7z5 - a9z - a9z3

Kauffman Polynomial:

a3z - a3z3 + a4z2 - 2a4z4 + a5z-1 - 5a5z + 6a5z3 - 4a5z5 - a6 + 5a6z2 - 6a6z4 + 2a6z6 - a6z8 + a7z-1 - 3a7z + 3a7z3 - 3a7z5 + 2a7z7 - a7z9 + 6a8z2 - 14a8z4 + 13a8z6 - 4a8z8 + 4a9z - 13a9z3 + 12a9z5 - a9z7 - a9z9 + a10z2 - 7a10z4 + 10a10z6 - 3a10z8 + a11z - 9a11z3 + 11a11z5 - 3a11z7 - a12z2 + 3a12z4 - a12z6

Khovanov Homology:

trqj r = -9 r = -8 r = -7 r = -6 r = -5 r = -4 r = -3 r = -2 r = -1 r = 0 j = -2                   1 j = -4                 2 1 j = -6               3     j = -8             3 2     j = -10           4 3       j = -12         3 3         j = -14       3 4           j = -16     2 4             j = -18   1 2               j = -20   2                 j = -22 1

Computer Talk. The data above can be recomputed by Mathematica using the package KnotTheory`. Following setup, the sample Mathematica session below reproduces most of the above data (Mathematica system prompts in blue, human input in red, Mathematica output in black):

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 30, 2005, 10:15:35)...
In[2]:=	Length[Skeleton[L]]
Out[2]=	2
In[3]:=	Show[DrawMorseLink[Link[11, NonAlternating, 149]]]
Out[3]=	-Graphics-
In[4]:=	PD[L = Link[11, NonAlternating, 149]]
Out[4]=	PD[X[8, 1, 9, 2], X[9, 19, 10, 18], X[6, 7, 1, 8], X[22, 19, 7, 20], > X[12, 5, 13, 6], X[3, 10, 4, 11], X[4, 15, 5, 16], X[16, 12, 17, 11], > X[20, 13, 21, 14], X[14, 21, 15, 22], X[17, 2, 18, 3]]
In[5]:=	GaussCode[L]
Out[5]=	GaussCode[{1, 11, -6, -7, 5, -3}, > {3, -1, -2, 6, 8, -5, 9, -10, 7, -8, -11, 2, 4, -9, 10, -4}]
In[6]:=	Jones[L][q]
Out[6]=	-(21/2) 3 4 6 7 7 6 5 2 -(3/2) q - ----- + ----- - ----- + ----- - ----- + ---- - ---- + ---- - q 19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2 q q q q q q q q
In[7]:=	A2Invariant[L][q]
Out[7]=	-32 -30 3 -20 2 2 -8 -6 -4 -q + q + --- + q + --- + --- + q - q + q 24 14 10 q q q
In[8]:=	HOMFLYPT[Link[11, NonAlternating, 149]][a, z]
Out[8]=	5 7 a a 3 5 7 9 3 3 5 3 7 3 -(--) + -- - a z - 5 a z + 4 a z - a z - a z - 3 a z + 3 a z - z z 9 3 7 5 > a z + a z
In[9]:=	Kauffman[Link[11, NonAlternating, 149]][a, z]
Out[9]=	5 7 6 a a 3 5 7 9 11 4 2 6 2 -a + -- + -- + a z - 5 a z - 3 a z + 4 a z + a z + a z + 5 a z + z z 8 2 10 2 12 2 3 3 5 3 7 3 9 3 > 6 a z + a z - a z - a z + 6 a z + 3 a z - 13 a z - 11 3 4 4 6 4 8 4 10 4 12 4 5 5 > 9 a z - 2 a z - 6 a z - 14 a z - 7 a z + 3 a z - 4 a z - 7 5 9 5 11 5 6 6 8 6 10 6 12 6 > 3 a z + 12 a z + 11 a z + 2 a z + 13 a z + 10 a z - a z + 7 7 9 7 11 7 6 8 8 8 10 8 7 9 9 9 > 2 a z - a z - 3 a z - a z - 4 a z - 3 a z - a z - a z
In[10]:=	Kh[L][q, t]
Out[10]=	-4 -2 1 2 1 2 2 4 3 q + q + ------ + ------ + ------ + ------ + ------ + ------ + ------ + 22 9 20 8 18 8 18 7 16 7 16 6 14 6 q t q t q t q t q t q t q t 4 3 3 4 3 3 2 3 2 > ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- 14 5 12 5 12 4 10 4 10 3 8 3 8 2 6 2 4 q t q t q t q t q t q t q t q t q t

Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11n149

L11n148 L11n150