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DurfeeSquare on IntegerPartition ​

The side of the Durfee square: the largest d with at least d parts of size at least d.

On IntegerPartition

Called as CombinatorialStat(x, "DurfeeSquare"). The head's page has its examples.

Live

FindStat St000183

The side length of the Durfee square of an integer partition.

ObjectValue
[]0
[1]1
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000183 has the rest.