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-numbers, diophantine exponent and factorisations of sturmian words
Caius Wojcik
We introduce the notion of -numbers and formal intercept of sturmian words, and derive from this study general factorisations formula for sturmian words. Sturmian words are defi…
Formal Intercept of Sturmian words
Caius Wojcik
We give a combinatorial definition of the second parameter describing Sturmian words, that we call formal intercept, as an infinite Ostrowski expansion. We recall the well-known pr…
On a new conjecture about super-monochromatic factorisations and ultimate periodicity
Caius Wojcik
We study a conjecture linking ultimate periodicity of infnite words to the existence of colorings on finite words avoiding monochromatic factorisation of suffixes, with the extra c…
Monochromatic factorisations of words and periodicity
Caïus Wojcik, Luca Q. Zamboni
In 2006 T. Brown asked the following question: Given a non-periodic infinite word with values in a non-empty set does there exist a finite colorin…