FirstBlockSecondOrSmallestNonsingletonMaximum on SetPartition
The smaller of the second element of the block holding 1 and the smallest closer; 1 when {1} is a block.
A closer is the greatest element of a non-singleton block.
Called as CombinatorialStat(x, "FirstBlockSecondOrSmallestNonsingletonMaximum"). The head's page has its examples.
Live
Distribution
Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St001784
The minimum of the smallest closer and the second element of the block containing 1 in a set partition.
| Object | Value |
|---|---|
{{1}} | 1 |
{{1,2}} | 2 |
{{1,2,3}} | 2 |
{{1},{2}} | 1 |
{{1,2,3,4}} | 2 |
{{1,2},{3}} | 2 |
{{1,3},{2}} | 3 |
{{1},{2,3}} | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001784 has the rest.