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MissingBoxCount on SkewPartition ​

The boxes of the outer partition that the shape leaves out: the size of the inner partition.

On SkewPartition

FindStat's St001438. The empty shape gives 0.

Called as CombinatorialStat(x, "MissingBoxCount"). 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 St001438

The number of missing boxes of a skew partition.

ObjectValue
[[1],[]]0
[[2],[]]0
[[3],[]]0
[[4],[]]0
[[5],[]]0
[[1,1],[]]0
[[2,1],[]]0
[[2,2],[]]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001438 has the rest.