|
The two links from that
table are given by minimal ten crossing almost alternating representations,
and all the other KLs with n=8 crossings are given by minimal nine crossing
representations.
For n=9 we have the following
results:
| 947 |
8*-2
0 |
8*2
1- |
949 |
-2 0:2:2 |
2 1-:2:2 |
| 9592 |
(3,2) -(2,2) |
(3,2)(3 1-,2) |
9602 |
(2 1,2)-(2,2) |
(2 1,2)(3
1-,2) |
| 9612 |
2:-2 0:-2
0 |
2 0.1-.2.2:2
0 |
9203 |
.(2,2-) |
.(2,2+-) |
| 9173 |
3,2,2,2- - |
3,2,2,3 1- |
9193 |
(2,2+)-(2,2) |
(2,2+)(3
1-,2) |
| 9213 |
.-(2,2) |
.(2,3 1-) |
From 42 non-alternating
knots for n=10, thirty nine of them can be given by almost alternating
minimal eleven crossing representations, and only three of them, 10152,
10153 and 10154, have 12-crossing minimal almost
alternating representations. They are given in the following table, which
does not include non-alternating knots described in general form as a1,a2,a3-
= a1,a2,a3+- or (a1,a2)
(a3,a4-) = (a1,a2) (a3,a4+-).
| 10152 |
(3,2)-(3,2) |
(3,2)(3 1-,2
1) |
10153 |
(3,2)-(21,2) |
(3,2)(3 1-,3) |
| 10154 |
(21,2)-(21,2) |
(2 1,2)(3
1-,3) |
10155 |
-3:2:2 |
2 1 1-0:2:2 |
| 10156 |
-3:2:2 0 |
2 1 1-0:2:2
0 |
10157 |
-3:2 0:2
0 |
2 1 1-0:2
0:2 0 |
| 10158 |
-3 0:2:2 |
2 1 1-:2:2 |
10159 |
-3 0:2:2
0 |
2 1 1-:2:2
0 |
| 10160 |
-3 0:2 0:2
0 |
2 1 1-:2
0:2 0 |
10161 |
3:-2 0:-2
0 |
2 0.1-.2.2:2
1 0 |
| 10162 |
-3 0:-2 0:-2
0 |
3:2 1-:2 |
10163 |
8*-3
0 |
8*2
1 1- |
| 10164 |
8*2:-2
0 |
8*2:2
1- |
10165 |
8*2:.-2
0 |
8*2:.2
1- |
  
|