The purpose of this paper is to study a statistic that is used to compare the similarity between two strings, which is first introduced by Michael Steele in 1982. It was proposed as an alternative to the length of the longest common subsequences, for which the variance problem is still open. Our results include moment asymptotics and distributional asymptotics for Steele's statistic and a variation of it in random words and random permutations. Comment: 17 pages
Discrete Mathematics & Theoretical Computer Science