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A Study Of Pseudo-Periodic And Pseudo-Bordered Words For Functions Beyond Identity And Involution, Manasi Kulkarni

Electronic Thesis and Dissertation Repository

Periodicity, primitivity and borderedness are some of the fundamental notions in combinatorics on words. Motivated by the Watson-Crick complementarity of DNA strands wherein a word (strand) over the DNA alphabet \{A, G, C, T\} and its Watson-Crick complement are informationally ``identical", these notions have been extended to consider pseudo-periodicity and pseudo-borderedness obtained by replacing the ``identity" function with ``pseudo-identity" functions (antimorphic involution in case of Watson-Crick complementarity). For a given alphabet $\Sigma$, an antimorphic involution $\theta$ is an antimorphism, i.e., $\theta(uv)=\theta(v) \theta(u)$ for all $u,v \in \Sigma^{*}$ and an involution, i.e., $\theta(\theta(u))=u$ for all $u \in \Sigma^{*}$. In this thesis, …