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.

Live

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.