2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75288We consider the distribution of the length of the longest subsequence avoiding a given pattern in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to avoiding the pattern 21. We show that there is some constant c such that the mean value of this length is asymptotic to twice the square root of c times n and that the distribution of the length is tightly concentrated around its mean. We observe some apparent connections between c and the Stanley-Wilf limit of the class of permutations avoiding the given pattern.14 pages (Reference list corrected)Combinatorics05A16; 05A05text