DurfeeCube on PlanePartition
The side of the largest cube in the array: the most diagonal entries d with the d-th at least d.
FindStat's St001451, the plane partition analogue of the Durfee square. Entries down the diagonal never increase, so once one falls short of its place every later one does.
Called as CombinatorialStat(x, "DurfeeCube"). The head's page has its examples.
Live
Distribution
Over PlanePartitions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001451
The side length of the largest cube contained in a plane partition.
| Object | Value |
|---|---|
[[1]] | 1 |
[[2]] | 1 |
[[3]] | 1 |
[[4]] | 1 |
[[5]] | 1 |
[[6]] | 1 |
[[7]] | 1 |
[[8]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001451 has the rest.