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ContainingSquareSide on IntegerPartition ​

The side of the smallest square that contains the diagram: the larger of the largest part and the number of parts.

On IntegerPartition

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

Live

FindStat St000784

The maximum of the length and the largest part of the integer partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000784 has the rest.