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On the superimposition of Christoffel words
Geneviève Paquin, Christophe Reutenauer
Initially stated in terms of Beatty sequences, the Fraenkel conjecture can be reformulated as follows: for a -letter alphabet A, with a fixed , there exists a unique b…
On the fixed point of the iterated pseudopalindromic closure
D. Jamet, G. Paquin, G. Richomme +1
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words wit…
On a generalization of Christoffel words: epichristoffel words
Genevieve Paquin
Sturmian sequences are well-known as the ones having minimal complexity over a 2-letter alphabet. They are also the balanced sequences over a 2-letter alphabet and the sequences de…
Infinite smooth Lyndon words
Genevieve Paquin
In a recent paper, Brlek, Jamet and Paquin showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: are they the only…
A characterization of balanced episturmian sequences
G. Paquin, L. Vuillon
It is well known that Sturmian sequences are the aperiodic sequences that are balanced over a 2-letter alphabet. They are also characterized by their complexity: they have exactly…