DistinctSubsetSums on IntegerPartition
Distinct sums of non-empty sub-multisets of the parts.
Follows FindStat's Sage code and its data, not its title: the "partial sums" it counts are the sums of arbitrary sub-multisets of the parts (the code runs over all subsets), not of the running prefixes.
Called as CombinatorialStat(x, "DistinctSubsetSums"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St000548
The number of different non-empty partial sums of an integer partition.
| Object | Value |
|---|---|
[] | 0 |
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000548 has the rest.