NoncrossingMergeableSingletonPairs on DyckPath
Pairs of singleton blocks of the path's noncrossing partition that can be merged into one block, leaving the partition noncrossing.
FindStat's St001932, under Biane's bijection (NoncrossingPartition): the ups whose matching downs share a run form a block.
Called as CombinatorialStat(x, "NoncrossingMergeableSingletonPairs"). The head's page has its examples.
Live
Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St001932
The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001932 has the rest.