48 citations · 248 across the 18 of their papers we have counts for
16 papers
Some Results on Digital Segments and Balanced Words
Alessandro De Luca, Gabriele Fici
We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give…
Maximal Closed Substrings
Golnaz Badkobeh, Alessandro De Luca, Gabriele Fici +1
A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a \emph{maximal closed substring} (MCS), w…
On the Lie complexity of Sturmian words
Alessandro De Luca, Gabriele Fici
Bell and Shallit recently introduced the Lie complexity of an infinite word as the function counting for each length the number of conjugacy classes of words whose elements are…
On the extremal values of the cyclic continuants of Motzkin and Straus
Alessandro De Luca, Luca Q. Zamboni
In a 1983 paper, G. Ramharter asks what are the extremal arrangements for the cyclic analogues of the regular and semi-regular continuants first introduced by T.S. Motzkin and E.G.…
Extremal values of semi-regular continuants and codings of interval exchange transformations
Alessandro De Luca, Marcia Edson, Luca Q. Zamboni
Given a set of positive integers and a partition , find the extremal denominators of the regular and semi-regular continued fraction $[0;x…
Characteristic Parameters and Special Trapezoidal Words
Alma D'Aniello, Alessandro De Luca
Following earlier work by Aldo de Luca and others, we study trapezoidal words and their prefixes, with respect to their characteristic parameters and (length of shortest un…
The sequence of open and closed prefixes of a Sturmian word
Alessandro De Luca, Gabriele Fici, Luca Q. Zamboni
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…
On Christoffel and standard words and their derivatives
Alma D'Aniello, Aldo de Luca, Alessandro De Luca
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…
Sturmian words and the Stern sequence
Aldo de Luca, Alessandro De Luca
Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A nat…
Aperiodic pseudorandom number generators based on infinite words
Lubomira Balkova, Michelangelo Bucci, Alessandro De Luca +2
In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior. We i…
Open and Closed Prefixes of Sturmian Words
Alessandro De Luca, Gabriele Fici
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…
Reversible Christoffel factorizations
Michelangelo Bucci, Alessandro De Luca, Luca Q. Zamboni
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 S…
Enumeration and Structure of Trapezoidal Words
Michelangelo Bucci, Alessandro De Luca, Gabriele Fici
Trapezoidal words are words having at most distinct factors of length for every . They therefore encompass finite Sturmian words. We give combinatorial characteri…
A generalized palindromization map in free monoids
Aldo de Luca, Alessandro De Luca
The palindromization map in a free monoid was introduced in 1997 by the first author in the case of a binary alphabet , and later extended by other authors to arbitrar…
A new characteristic property of rich words
Michelangelo Bucci, Alessandro De Luca, Amy Glen +1
Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer in arXiv:0801.1656, rich words constitute a new class of finite and infinite…
A connection between palindromic and factor complexity using return words
Michelangelo Bucci, Alessandro De Luca, Amy Glen +1
In this paper we prove that for any infinite word W whose set of factors is closed under reversal, the following conditions are equivalent: (I) all complete returns to palindromes…