Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

Anant Godbole, Ph.D.

Committee Members

Teresa Haynes, Ph.D., Nicole Lewis, Ph.D.


Previous work by Flaxman (2004) and Biers-Ariel et al. (2018) focused on the number of distinct words embedded in a string of words of length n. In this thesis, we will extend this work to permutations, focusing on the maximum number of distinct permutations contained in a permutation on [n] = {1,2,...,n} and on the expected number of distinct permutations contained in a random permutation on [n]. We further considered the problem where repetition of subsequences are as a result of the occurrence of (Type A and/or Type B) replications. Our method of enumerating the Type A replications causes double counting and as a result causes the count of the number of distinct sequences to go down.

Document Type

Thesis - unrestricted


Copyright by the authors.