scholarly journals Lyndon Words, the Three Squares Lemma, and Primitive Squares

2020 ◽  
pp. 265-273
Author(s):  
Hideo Bannai ◽  
Takuya Mieno ◽  
Yuto Nakashima
Keyword(s):  
Lyndon Words

scholarly journals Sturmian words, Lyndon words and trees

1997 ◽  
Vol 178 (1-2) ◽  
pp. 171-203 ◽  
Author(s):  
Jean Berstel ◽  
Aldo de Luca
Keyword(s):  
Sturmian Words ◽  
Lyndon Words

scholarly journals DETERMINING EQUATIONS FOR HIGHER-ORDER DECOMPOSITIONS OF EXPONENTIAL OPERATORS

1995 ◽  
Vol 09 (25) ◽  
pp. 3241-3268 ◽  
Author(s):  
ZENGO TSUBOI ◽  
MASUO SUZUKI
Keyword(s):  
General Scheme ◽  
Higher Order ◽  
Explicit Formulas ◽  
Decomposition Theory ◽  
Lyndon Words

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.

The Number of Irreducible Polynomials and Lyndon Words with Given Trace

2001 ◽  
Vol 14 (2) ◽  
pp. 240-245 ◽  
Author(s):  
F. Ruskey ◽  
C. R. Miers ◽  
J. Sawada
Keyword(s):  
Irreducible Polynomials ◽  
Lyndon Words

scholarly journals On generalized Lyndon words

2019 ◽  
Vol 777 ◽  
pp. 232-242 ◽  
Author(s):  
Francesco Dolce ◽  
Antonio Restivo ◽  
Christophe Reutenauer
Keyword(s):  
Lyndon Words

scholarly journals On a factorization of graded Hopf algebras using Lyndon words

2007 ◽  
Vol 314 (1) ◽  
pp. 324-343 ◽  
Author(s):  
M. Graña ◽  
I. Heckenberger
Keyword(s):  
Hopf Algebras ◽  
Lyndon Words

scholarly journals Monomial algebras defined by Lyndon words

2014 ◽  
Vol 403 ◽  
pp. 470-496 ◽  
Author(s):  
Tatiana Gateva-Ivanova ◽  
Gunnar Fløystad
Keyword(s):  
Monomial Algebras ◽  
Lyndon Words

scholarly journals Lyndon words, polylogarithms and the Riemann ζ function

2000 ◽  
Vol 217 (1-3) ◽  
pp. 273-292 ◽  
Author(s):  
Hoang Ngoc Minh ◽  
Michel Petitot
Keyword(s):  
Riemann Ζ Function ◽  
Lyndon Words

scholarly journals On morphisms preserving infinite Lyndon words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Gwenael Richomme
Keyword(s):  
Free Monoid ◽  
Infinite Words ◽  
International Audience ◽  
Lyndon Words

International audience 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 we study morphisms preserving infinite Lyndon words and morphisms preserving the order on infinite words. We characterize them and show relations with morphisms preserving Lyndon words or the order on finite words. We also briefly study morphisms preserving border-free words and those preserving the radix order.

scholarly journals Gray code order for Lyndon words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Vincent Vajnovszki
Keyword(s):  
Gray Code ◽  
Time Algorithm ◽  
Positive Answer ◽  
Combinatorics On Words ◽  
International Audience ◽  
Lyndon Words

International audience At the 4th Conference on Combinatorics on Words, Christophe Reutenauer posed the question of whether the dual reflected order yields a Gray code on the Lyndon family. In this paper we give a positive answer. More precisely, we present an O(1)-average-time algorithm for generating length n binary pre-necklaces, necklaces and Lyndon words in Gray code order.

scholarly journals Finely homogeneous computations in free Lie algebras

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Philippe Andary
Keyword(s):  
Lie Algebras ◽  
Vector Fields ◽  
Simple Algorithm ◽  
Lexicographic Order ◽  
Worst Case ◽  
Free Lie Algebras ◽  
International Audience ◽  
Lyndon Word ◽  
The One ◽  
Lyndon Words

International audience We first give a fast algorithm to compute the maximal Lyndon word (with respect to lexicographic order) of \textitLy_α (A) for every given multidegree alpha in \textbfN^k. We then give an algorithm to compute all the words living in \textitLy_α (A) for any given α in \textbfN^k. The best known method for generating Lyndon words is that of Duval [1], which gives a way to go from every Lyndon word of length n to its successor (with respect to lexicographic order by length), in space and worst case time complexity O(n). Finally, we give a simple algorithm which uses Duval's method (the one above) to compute the next standard bracketing of a Lyndon word for lexicographic order by length. We can find an interesting application of this algorithm in control theory, where one wants to compute within the command Lie algebra of a dynamical system (letters are actually vector fields).

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