Nyldon words

Charlier, Émilie; Philibert, Manon; Stipulanti, Manon

doi:10.1016/j.jcta.2019.04.002

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…Several variations of Lyndon words have been considered lately: generalized Lyndon [26], anti-Lyndon [15], inverse Lyndon [4], and Nyldon [6]. In this text, we will use the second.…”

Section: Wordsmentioning

confidence: 99%

String Attractors of Fixed Points of k-Bonacci-Like Morphisms

Gheeraert

Romana

Stipulanti

2023

Lecture Notes in Computer Science

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Firstly studied by Kempa and Prezza in 2018 as the cement of text compression algorithms, string attractors have become a compelling object of theoretical research within the community of combinatorics on words. In this context, they have been studied for several families of finite and infinite words. In this paper, we obtain string attractors of prefixes of particular infinite words generalizing k-bonacci words (including the famous Fibonacci word) and obtained as fixed points of k-bonacci-like morphisms. In fact, our description involves the numeration systems classically derived from the considered morphisms.

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“…Several variations of Lyndon words have been considered lately: generalized Lyndon [26], anti-Lyndon [15], inverse Lyndon [4], and Nyldon [6]. In this text, we will use the second.…”

Section: Wordsmentioning

confidence: 99%

String Attractors of Fixed Points of k-Bonacci-Like Morphisms

Gheeraert

Romana

Stipulanti

2023

Lecture Notes in Computer Science

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“…More recently Lyndon words found a renewed theoretical interest and several variants of them have been introduced and investigated with different motivations [9,18,19]. A related field studies the combinatorial and algorithmic properties of necklaces, that are powers of Lyndon words, and their prefixes or prenecklaces [8].…”

Section: Introductionmentioning

confidence: 99%

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

Bonizzoni

Felice

Zaccagnino

et al. 2020

Language and Automata Theory and Applications

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Lyndon words have been largely investigated and showned to be a useful tool to prove interesting combinatorial properties of words. In this paper we state new properties of both Lyndon and inverse Lyndon factorizations of a word w, with the aim of exploring their use in some classical queries on w.The main property we prove is related to a classical query on words. We prove that there are relations between the length of the longest common extension (or longest common prefix) lcp(x, y) of two different suffixes x, y of a word w and the maximum length M of two consecutive factors of the inverse Lyndon factorization of w. More precisely, M is an upper bound on the length of lcp(x, y). This result is in some sense stronger than the compatibility property, proved by Mantaci, Restivo, Rosone and Sciortino for the Lyndon factorization and here for the inverse Lyndon factorization. Roughly, the compatibility property allows us to extend the mutual order between local suffixes of (inverse) Lyndon factors to the suffixes of the whole word.A main tool used in the proof of the above results is a property that we state for factors m i with nonempty borders in an inverse Lyndon factorization: a nonempty border of m i cannot be a prefix of the next factor m i+1 . The last property we prove shows that if two words share a common overlap, then their Lyndon factorizations can be used to capture the common overlap of the two words.The above results open to the study of new applications of Lyndon words and inverse Lyndon words in the field of string comparison.

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“…Note that Nyldon words, introduced by Grinberg in [11], also provide a factorization of the free monoid (see [7]), but they are not generalized Lyndon words. Inverse Lyndon words introduced in [4] are not generalized Lyndon words neither, while anti-Lyndon words (introduced in the same paper) with respect to a lexicographical order < can be viewed as classical Lyndon words with respect to the order< (see also Example 9 later).…”

Section: Introductionmentioning

confidence: 99%

On generalized Lyndon words

Dolce

Restivo

Reutenauer

2019

Theoretical Computer Science

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A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as a nonincreasing factorization of generalized Lyndon words. We give new characterizations of the first and the last factor in this factorization as well as new characterization of generalized Lyndon words. We also give more specific results on two special cases: the classical one and the one arising from the alternating lexicographical order.

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Nyldon words

Cited by 9 publications

References 13 publications

String Attractors of Fixed Points of k-Bonacci-Like Morphisms

String Attractors of Fixed Points of k-Bonacci-Like Morphisms

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

On generalized Lyndon words

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