The longest common subsequence (LCS) problem, a long‐standing challenge in computer science and bioinformatics, seeks to identify the maximum sequence of characters shared by multiple strings ...

It follows from results concerning the longest increasing subsequence of a random permutation that the law of large numbers cannot hold for $Z_ {n,k_ {n}}$ if $k_ {n}\geq cn^ {1/2}$, with c > 2.