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ProperBlocks on Permutation ​

Windows p(i), ..., p(j) of two or more entries whose values are consecutive integers, the whole word excepted.

On Permutation

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

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Distribution

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FindStat St001160

The number of proper blocks (or intervals) of a permutations.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001160 has the rest.