FrobeniusRank on SkewPartition
The fewest border strips that the shape divides into.
FindStat's St001597. A strip is a path of cells going up or right, so the fewest strips are the cells less the most pairs of neighbors that no cell takes twice as the one before and as the one after. Those pairs lie between consecutive diagonals, in runs, and a run of m cells gives floor(m / 2). A connected shape of one strip is a border strip. The empty shape gives 0.
Called as CombinatorialStat(x, "FrobeniusRank"). The head's page has its examples.
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Distribution
Over SkewPartitions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001597
The Frobenius rank of a skew partition.
| Object | Value |
|---|---|
[[1],[]] | 1 |
[[2],[]] | 1 |
[[3],[]] | 1 |
[[4],[]] | 1 |
[[5],[]] | 1 |
[[6],[]] | 1 |
[[7],[]] | 1 |
[[1,1],[]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001597 has the rest.