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Counting (Watson-Crick) palindromes in Watson-Crick conjugates
Date Issued
01-05-2022
Author(s)
Abstract
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. In this paper, we study a generalization of conjugates of a word that incorporate the notion of WK-involution θ called θ-conjugates or WK-conjugates. We consider some general properties of the set Cθ(w), i.e., the set of θ-conjugates of a word w. We characterize words with the same set of θ-conjugates and also provide words where the set of conjugates of a word is equal to the set of θ-conjugates of the word. 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 find the structure of words that have at least one (WK-)palindrome in Cθ(w).
Volume
285