θ共轭中的θ回文
Theta palindromes in theta conjugates
摘要：
DNA串是沃森-克里克（WK）回文，当它的反向的互补等于它自己。沃森-克里克映射$θ$是一个对合，也是一个反态。词的$θ$ -轭合是词的轭合的一种概括，它包含了WK-对合$θ$的概念。本文研究了词$w$的回文和Watson-Crick回文（也称为$θ$ -回文）在词的共轭集合和$θ$ -共轭集合中的分布。我们还考虑了集合$C_θ(w)$的一些一般性质，即，词$w$的$θ$ -共轭的集合，并且特征化词$w$，使得$|C_θ(w)|=|w|+1$，即，具有$C_θ(w)$中的最大元素数。我们还发现了在$C_θ(w)$中至少有一个（WK）-回文的词的结构。
英文摘要：
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 $C_θ(w)$.
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