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<p>The conjugate or a cyclic permutation of a word is obtained by decomposing the word into two adjacent factors and swapping them. The adjacent factor swap of a word is a generalization of the concept of cyclic permutation of a word wherein, a subword of the word is decomposed in to two non-overlapping factor parts and swapped. Since there can be multiple ways in which a word can be divided into factors, the adjacent factor swap of a word forms a set. In this paper, we study some properties of adjacent factor swap of a word. We characterize words with the minimum and the maximum number of elements in their adjacent factor swap. We then study the distribution of palindromes in the adjacent factor swap of a word. For a palindrome <i>w</i>, we give a tight bound on the maximum number of palindromes in the adjacent swap of <i>w</i>, if the number of distinct letters in <i>w</i> is half its length. We also provide a slack bound on the maximum number of palindromes in the adjacent swap of a given word.</p>

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Palindromes in adjacent factor swap of a word

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Kalpana Mahalingam

摘要

The conjugate or a cyclic permutation of a word is obtained by decomposing the word into two adjacent factors and swapping them. The adjacent factor swap of a word is a generalization of the concept of cyclic permutation of a word wherein, a subword of the word is decomposed in to two non-overlapping factor parts and swapped. Since there can be multiple ways in which a word can be divided into factors, the adjacent factor swap of a word forms a set. In this paper, we study some properties of adjacent factor swap of a word. We characterize words with the minimum and the maximum number of elements in their adjacent factor swap. We then study the distribution of palindromes in the adjacent factor swap of a word. For a palindrome w, we give a tight bound on the maximum number of palindromes in the adjacent swap of w, if the number of distinct letters in w is half its length. We also provide a slack bound on the maximum number of palindromes in the adjacent swap of a given word.