Abstract:
In this thesis, we investigate the properties of the longest common subsequences in random words, examine upper and lower bounds for the expected value of the longest common subsequences in this setting, and discuss the behavior of the asymptotic order of the longest common subsequences's variance. Besides this, we also study the relationship between longest common subsequences and longest increasing subsequences in random permutations and discuss some properties of the matrix L (n) that is generated by the length of the longest common subsequences of permutations. Our aim is to understand the details of the theory of the longest common subsequences whose study begun in 1970's, draw attention to the progress about the longest common subsequences in the recent studies, and state some open problems about the subject
