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Author Cassaigne, Julien ♦ Karhumaki, Juhani ♦ Puzynina, Svetlana
Source Hyper Articles en Ligne (HAL)
Content type Text
Publisher Elsevier
File Format PDF
Language English
Subject Keyword infinite words ♦ palindromes ♦ rich words ♦ k-abelian equivalence ♦ math ♦ Mathematics [math]/Combinatorics [math.CO]
Abstract 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 ncontaining Theta(n(2)) distinct k-abelian palindromes as their factors.
ISSN 08905401
Educational Use Research
Learning Resource Type Article
Publisher Date 2018-06-01
e-ISSN 10902651
Journal Information and Computation
Volume Number 260
Page Count 10
Starting Page 89
Ending Page 98