Theta palindromes in theta conjugates

08/01/2020

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by   Kalpana Mahalingam, et al.

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A DNA string is a Watson-Crick (WK) palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping θ is an involution that is also an antimorphism. θ-conjugates of a word is a generalisation of conjugates of a word that incorporates the notion of WK-involution θ. In this paper, we study the distribution of palindromes and Watson-Crick palindromes, also known as θ-palindromes among both the set of conjugates and θ-conjugates of a word w. We also consider some general properties of the set C_θ(w), i.e., the set of θ-conjugates of a word w, and characterize words w such that |C_θ(w)|=|w|+1, i.e., with the maximum number of elements in C_θ(w). We also find the structure of words that have at least one (WK)-palindrome in C_θ(w).