InterlacingPartitionCount on IntegerPartition
The number of partitions that interlace this one: the product over the parts of the gap to the next part (0 after the last) plus 1.
Called as CombinatorialStat(x, "InterlacingPartitionCount"). The head's page has its examples.
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Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001814
The number of partitions interlacing the given partition.
| Object | Value |
|---|---|
[] | 1 |
[1] | 2 |
[2] | 3 |
[3] | 4 |
[4] | 5 |
[5] | 6 |
[6] | 7 |
[7] | 8 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001814 has the rest.