SkewConnectedComponentCount on SkewPartition
The connected components of the shape: rows that start a component, the first row and every row that shares no column with the row above.
FindStat's St001490, the components of the cell poset. Row i meets the row above in a column exactly when λᵢ exceeds μᵢ₋₁. The empty shape gives 0.
Called as CombinatorialStat(x, "SkewConnectedComponentCount"). The head's page has its examples.
Live
Distribution
Over SkewPartitions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001490
The number of connected components of a skew partition.
| Object | Value |
|---|---|
[[1],[]] | 1 |
[[2],[]] | 1 |
[[3],[]] | 1 |
[[4],[]] | 1 |
[[5],[]] | 1 |
[[1,1],[]] | 1 |
[[2,1],[]] | 1 |
[[2,2],[]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001490 has the rest.