Das Gitterpunkt Problem
Overview: This was a project I did in the Spring of 2001 to learn backtrack enumeration techniques. It is a Ramsey problem. The table can be interpreted as the minimum number of integer vectors in k dimensions so that there must exist an n-set of points that average to zero.
Results:
| Points/Dimension |
1 |
2 |
3 |
4 |
5 |
6 |
| 1 Point |
0 |
0 |
0 |
0 |
0 |
0 |
| 2 Points |
2 |
4 |
8 |
16 |
32 |
64 |
| 3 Points |
4 |
8 |
18 |
40 |
76 |
140 |
| 4 Points |
6 |
12 |
24 |
48 |
96 |
192 |
| 5 Points |
8 |
16 |
36 |
73 |
149 |
256 |
| 6 Points |
10 |
20 |
40 |
80 |
160 |
320 |
| 7 Points |
12 |
24 |
54 |
106 |
192 |
384 |
| 8 Points |
14 |
28 |
56 |
112 |
224 |
448 |
| 9 Points |
16 |
32 |
64 |
128 |
256 |
512 |
All entrys without a link are of the form {0,1}^* x (Dimension-1).
Code:
Data:
Papers: rough draft