Among their many remarkable properties, Christoffel words are known to be linked
to Markov numbers, i.e., positive integer solutions to the equation
$x^2+y^2+z^2=3xyz$.
We express Markov numbers as coefficients of Christoffel words for a …
We introduce and study natural derivatives for Christoffel and finite standard
words, as well as for characteristic Sturmian words. These derivatives, which
are realized as inverse images under suitable morphisms, preserve the
aforementioned classes …
Central, standard, and Christoffel words are three strongly interrelated classes
of binary finite words which represent a finite counterpart to characteristic
Sturmian words. A natural arithmetization of the theory is obtained by
representing …
We define a family of natural decompositions of Sturmian words in Christoffel
words, called reversible Christoffel (RC) factorizations. They arise from the
observation that two Sturmian words with the same language have (almost always) …
In this paper we present three new characterizations of Sturmian
words based on the lexicographic ordering of their factors.
In this note we present some results on the Calkin-Wilf tree of irreducible
fractions, giving an insight on the duality relating it to the Stern-Brocot
tree, and proving noncommutative versions of known results relating labels of
the Calkin Wilf …