A finite word is closed if it contains a factor that occurs both as a prefix and
as a suffix but does not have internal occurrences, otherwise it is open. We are
interested in the oc-sequence of a word, which is the binary sequence whose
*n*-th …
A finite word is closed if it contains a factor that occurs both as a prefix and
as a suffix but does not have internal occurrences, otherwise it is open. We are
interested in the oc-sequence of a word, which is the binary sequence whose
*n*-th …
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 …
In this paper we introduce the *well distributed occurrences* (WDO)
combinatorial property for infinite words, which guarantees good
behavior (no lattice structure) in some related pseudorandom number
generators. An infinite word $u$ on a $d$-ary …
A word is closed if it contains a proper factor that occurs both as a prefix and
as a suffix but does not have internal occurrences, otherwise it is open. We
deal with the sequence of open and closed prefixes of Sturmian words and prove
that …
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) …
We study some structural and combinatorial properties of Sturmian palindromes,
i.e., palindromic finite factors of Sturmian words. In particular, we give a
formula which permits to compute in an exact way the number of Sturmian
palindromes of …