Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Lyndon words and Christoffel words
View through CrossRef
Abstract
We give the basic properties of Lyndon words. Lower Christoffel words are particular Lyndon words. They are maximal for the lexicographical order among Lyndon words of a given slope (Borel and Laubie). The function which maps a lower Christoffel word onto its slope is increasing with respect to the lexicographical order (Borel and Laubie). Lower Christoffel words are the Lyndon words which are equilibrated (Melançon).
Title: Lyndon words and Christoffel words
Description:
Abstract
We give the basic properties of Lyndon words.
Lower Christoffel words are particular Lyndon words.
They are maximal for the lexicographical order among Lyndon words of a given slope (Borel and Laubie).
The function which maps a lower Christoffel word onto its slope is increasing with respect to the lexicographical order (Borel and Laubie).
Lower Christoffel words are the Lyndon words which are equilibrated (Melançon).
Related Results
Balance properties on Christoffel words and applications
Balance properties on Christoffel words and applications
Propriétés d'équilibre sur les mots de Christoffel et applications.
De nombreux chercheurs se sont intéressés à la Combinatoire des mots aussi bien d'un point de vu...
Lyndon Words and Christoffel Words
Lyndon Words and Christoffel Words
This chapter covers the lexicographical ordering of lower Christoffel words, which is equivalent to the ordering by their slopes (Borel and Laubie). Lower Christoffel words are par...
From Christoffel Words to Markoff Numbers
From Christoffel Words to Markoff Numbers
Christoffel introduced in 1875 a special class of words on a binary alphabet, linked to continued fractions. Some years laterMarkoff published his famous theory, called nowMarkoff ...
Enhancing Graph-based Machine Learning through Lyndon Partial Words
Enhancing Graph-based Machine Learning through Lyndon Partial Words
Objectives: This study integrates the combinatorial properties of Lyndon partial words with Graph-Based Machine Learning (GBML) to develop an innovative approach for sequence analy...
Practical Evaluation of Lyndon Factors via Alphabet Reordering
Practical Evaluation of Lyndon Factors via Alphabet Reordering
We evaluate the influence of different alphabet orderings on the Lyndon factorization of a string. Experiments with Pizza&Chili datasets show that for most alphabet reorderings...
Words and Quadratic Numbers
Words and Quadratic Numbers
This chapter offers an overview of words and quadratic numbers, and in particular ordering the conjugates of a Christoffel word. Within this topic the reader learns that the revers...
Numerology
Numerology
This chapter gives several examples, which may help the reader to work in concrete terms with Markoff numbers, Christoffel words, Markoff constants, and quadratic forms. In particu...
On morphisms preserving infinite Lyndon words
On morphisms preserving infinite Lyndon words
In a previous paper, we characterized free monoid morphisms preserving finite Lyndon words. In particular, we proved that such a morphism preserves the order on finite words. Here ...