 L11a358 |
 L11a360 |
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The 2-Component Link L11a359Visit L11a359's page at Knotilus! |
 DrawMorseLink |
| PD Presentation: | X12,1,13,2 X14,3,15,4 X20,10,21,9 X16,6,17,5 X22,15,11,16 X8,18,9,17 X18,8,19,7 X6,20,7,19 X4,22,5,21 X2,11,3,12 X10,13,1,14 |
| Gauss Code: | {{1, -10, 2, -9, 4, -8, 7, -6, 3, -11}, {10, -1, 11, -2, 5, -4, 6, -7, 8, -3, 9, -5}} |
| Jones Polynomial: | q-9/2 - 3q-7/2 + 6q-5/2 - 10q-3/2 + 13q-1/2 - 16q1/2 + 15q3/2 - 14q5/2 + 10q7/2 - 6q9/2 + 3q11/2 - q13/2 |
| A2 (sl(3)) Invariant: | - q-14 + q-12 - 2q-8 + 3q-6 - q-4 + 3 - q2 + 4q4 + 2q8 + 2q10 - 3q12 + 2q14 - q18 + q20 |
| HOMFLY-PT Polynomial: | - a-5z - a-5z3 - a-3z-1 + a-3z3 + a-3z5 + a-1z-1 + 3a-1z + 4a-1z3 + 2a-1z5 + az3 + az5 - a3z - a3z3 |
| Kauffman Polynomial: | 2a-7z3 - a-7z5 - 2a-6z2 + 6a-6z4 - 3a-6z6 + 3a-5z - 9a-5z3 + 11a-5z5 - 5a-5z7 + a-4z2 - 7a-4z4 + 9a-4z6 - 5a-4z8 + a-3z-1 + a-3z - 9a-3z3 + 7a-3z5 - 3a-3z9 - a-2 + 5a-2z2 - 15a-2z4 + 15a-2z6 - 6a-2z8 - a-2z10 + a-1z-1 - 5a-1z + 12a-1z3 - 14a-1z5 + 12a-1z7 - 6a-1z9 + 5z2 - 11z4 + 14z6 - 5z8 - z10 - 2az + 3az3 + 4az7 - 3az9 + a2z2 - 6a2z4 + 10a2z6 - 4a2z8 + a3z - 7a3z3 + 9a3z5 - 3a3z7 - 2a4z2 + 3a4z4 - a4z6 |
| Khovanov Homology: |
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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, Alternating, 359]]] |
| |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 359]] |
Out[4]= | PD[X[12, 1, 13, 2], X[14, 3, 15, 4], X[20, 10, 21, 9], X[16, 6, 17, 5], > X[22, 15, 11, 16], X[8, 18, 9, 17], X[18, 8, 19, 7], X[6, 20, 7, 19], > X[4, 22, 5, 21], X[2, 11, 3, 12], X[10, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -9, 4, -8, 7, -6, 3, -11},
> {10, -1, 11, -2, 5, -4, 6, -7, 8, -3, 9, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(9/2) 3 6 10 13 3/2 5/2
q - ---- + ---- - ---- + ------- - 16 Sqrt[q] + 15 q - 14 q +
7/2 5/2 3/2 Sqrt[q]
q q q
7/2 9/2 11/2 13/2
> 10 q - 6 q + 3 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -14 -12 2 3 -4 2 4 8 10 12 14
3 - q + q - -- + -- - q - q + 4 q + 2 q + 2 q - 3 q + 2 q -
8 6
q q
18 20
> q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 359]][a, z] |
Out[8]= | 3 3 3 5 5
1 1 z 3 z 3 z z 4 z 3 3 3 z 2 z
-(----) + --- - -- + --- - a z - -- + -- + ---- + a z - a z + -- + ---- +
3 a z 5 a 5 3 a 3 a
a z a a a a
5
> a z |
In[9]:= | Kauffman[Link[11, Alternating, 359]][a, z] |
Out[9]= | 2 2 2
-2 1 1 3 z z 5 z 3 2 2 z z 5 z
-a + ---- + --- + --- + -- - --- - 2 a z + a z + 5 z - ---- + -- + ---- +
3 a z 5 3 a 6 4 2
a z a a a a a
3 3 3 3
2 2 4 2 2 z 9 z 9 z 12 z 3 3 3 4
> a z - 2 a z + ---- - ---- - ---- + ----- + 3 a z - 7 a z - 11 z +
7 5 3 a
a a a
4 4 4 5 5 5 5
6 z 7 z 15 z 2 4 4 4 z 11 z 7 z 14 z
> ---- - ---- - ----- - 6 a z + 3 a z - -- + ----- + ---- - ----- +
6 4 2 7 5 3 a
a a a a a a
6 6 6 7 7
3 5 6 3 z 9 z 15 z 2 6 4 6 5 z 12 z
> 9 a z + 14 z - ---- + ---- + ----- + 10 a z - a z - ---- + ----- +
6 4 2 5 a
a a a a
8 8 9 9
7 3 7 8 5 z 6 z 2 8 3 z 6 z 9
> 4 a z - 3 a z - 5 z - ---- - ---- - 4 a z - ---- - ---- - 3 a z -
4 2 3 a
a a a
10
10 z
> z - ---
2
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 2 1 4 2 6 4 6 7
9 + 8 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + - + ---- +
10 5 8 4 6 4 6 3 4 3 4 2 2 2 t 2
q t q t q t q t q t q t q t q t
2 4 4 2 6 2 6 3 8 3 8 4
> 7 q t + 8 q t + 7 q t + 8 q t + 4 q t + 6 q t + 2 q t +
10 4 10 5 12 5 14 6
> 4 q t + q t + 2 q t + q t |
| Dror Bar-Natan: The Knot Atlas: The Thistlethwaite Link Table: The Link L11a359 |
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