Counting (Watson-Crick) palindromes in Watson-Crick conjugates

A DNA string is a Watson-Crick (WK-)palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping theta 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 theta called theta-conjugates or WK-conjugates. We consider some general properties of the set C theta(w), i.e., the set of theta-conjugates of a word w. We characterize words with the same set of theta-conjugates and also provide words where the set of conjugates of a word is equal to the set of theta-conjugates of the word. We study the distribution of palindromes and Watson-Crick palindromes, also known as theta-palindromes, among both the set of conjugates and theta-conjugates of a word w. We also find the structure of words that have at least one (WK-)palindrome in C theta(w).(c) 2021 Elsevier Inc. All rights reserved.