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MaximalBlockDifference on SetPartition ​

The largest difference between two elements of one block.

On SetPartition

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

Live

FindStat St000503

The maximal difference between two elements in a common block.

ObjectValue
{{1,2}}1
{{1,2,3}}2
{{1},{2}}0
{{1,2,3,4}}3
{{1,2},{3}}1
{{1,3},{2}}2
{{1},{2,3}}1
{{1,2,3,4,5}}4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000503 has the rest.