LongestIncreasingSubsequence on Permutation

The length of a longest increasing subsequence.

On Permutation

By patience sorting: the number of piles. Checked against the piles algorithm over every permutation of 1..6.

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

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Distribution

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Sizes 1 to

FindStat St000062

The length of the longest increasing subsequence of the permutation.

Object	Value
[1]	1
[1,2]	2
[2,1]	1
[1,2,3]	3
[1,3,2]	2
[2,1,3]	2
[2,3,1]	2
[3,1,2]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000062 has the rest.