A1 Journal article – refereed
On k-abelian palindromes

List of Authors: Julien Cassaigne, Juhani Karhumäki, Svetlana Puzynina
Publisher: Elsevier Inc.
Publication year: 2018
Journal: Information and Computation
Journal name in source: Information and Computation
Volume number: 260
eISSN: 1090-2651


A word is called a palindrome if it is equal to its reversal. In the paper we consider a k-abelian modification of this notion. Two words are called k-abelian equivalent if they contain the same number of occurrences of each factor of length at most k. We say that a word is a k-abelian palindrome if it is k-abelian equivalent to its reversal. A question we deal with is the following: how many distinct palindromes can a word contain? It is well known that a word of length n can contain at most n+1

distinct palindromes as its factors; such words are called rich. On the other hand, there exist infinite words containing only finitely many distinct palindromes as their factors; such words are called poor. We show that in the k-abelian case there exist infinite words containing finitely many distinct k-abelian palindromic factors. For rich words we show that there exist finite words of length n containing Θ(n2)

distinct k-abelian palindromes as their factors.

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Last updated on 2019-29-01 at 11:26