A decreasing subsequence of a permutation is a subsequence of the permutation whose elements decrease. For the permutation $\pi$ equal to (8, 2, 1, 6, 5, 7, 4, 3, 9), (8, 7, 3) and (8, 6, 5, 4, 3) are decreasing subsequences. You may verify that the second subsequence is the longest possible decreasing subsequence of $\pi$.

See also increasing permutation subsequence.