We enumerate (in lexicographic order) all the terminal Schur $k$-partitions, i.e., such that it is not possible to extend the partition by placing the next successive integer while keeping the sum-free property.
To reduce the size of the data we regroup such partitions into cluster. The for each cluster we determine the mean and the maximal partition length :
Type |
Colors $k$ |
Terminal partitions |
Cluster size |
Correlation |
Files |
Strong |
3 |
138 |
10 |
0.66 |
data png |
Strong |
4 |
92 292 017 |
1 000 000 |
-0.17 |
data png |
Weak |
3 |
8 066 |
100 |
0.88 |
data png |
Weak |
4 |
536 994 391 720 |
1 000 000 000 |
0.69 |
data png |
Source code is availbale on
GitHub.
, vol. 7832 of