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
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 particular Lyndon words. They are maximum for the lexicographical order among Lyndon words of a given slope (Borel and Laubie). They are, together with the upper Christoffel words, the only unbordered finite Sturmian words (Chuan). They are exactly the Lyndon words which are Sturmian words (Berstel and de Luca). The standard factorization of a lower Christoffel word is obtained by cutting before the smallest lexicographical suffix. Finally, they are exactly the Lyndon words which are equilibrated (Melançon).
Title: Lyndon Words and Christoffel Words
Description:
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 particular Lyndon words.
They are maximum for the lexicographical order among Lyndon words of a given slope (Borel and Laubie).
They are, together with the upper Christoffel words, the only unbordered finite Sturmian words (Chuan).
They are exactly the Lyndon words which are Sturmian words (Berstel and de Luca).
The standard factorization of a lower Christoffel word is obtained by cutting before the smallest lexicographical suffix.
Finally, they are exactly the Lyndon words which are equilibrated (Melançon).
Related Results
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...
Computing Longest Lyndon Subsequences and Longest Common Lyndon Subsequences
Computing Longest Lyndon Subsequences and Longest Common Lyndon Subsequences
AbstractGiven a string T of length n whose characters are drawn from an ordered alphabet of size $$\sigma $$
σ
, its longest Lyndon subsequence is...
Computing Longest Lyndon Subsequences and Longest Common Lyndon Subsequences
Computing Longest Lyndon Subsequences and Longest Common Lyndon Subsequences
Abstract
Given a string T with length n whose characters are drawn from an ordered alphabet of size σ, its longest Lyndon subsequence is a longest subsequence of T that is ...
Lyndon Interpolation holds for the Prenex ⊃ Prenex Fragment of Gödel Logic
Lyndon Interpolation holds for the Prenex ⊃ Prenex Fragment of Gödel Logic
First-order interpolation properties are notoriously hard to determine, even for logics where propositional interpolation is more or less obvious. One of the most prominent example...
Quantitative Evaluation of Vocabulary Emotional Color in Language Teaching
Quantitative Evaluation of Vocabulary Emotional Color in Language Teaching
Objective. In real communication, the context is complex and changeable and the color and meaning of some words will wander in the context. The development and changes of words are...
Stern–Brocot Tree
Stern–Brocot Tree
Christoffel words have a strong connection with continued fractions of rational numbers, as was recognized by Christoffel. They are in some sense equivalent to them, being a way to...
Barry Lyndon
Barry Lyndon
Set in the second half of the eighteenth century, Barry Lyndon is the fictional autobiography of an adventurer and rogue whom the reader is led to distrust from the very beginning....