A de Bruijn sequence over a finite alphabet of span n is a cyclic string such that all words of length n appear exactly once as factors of this sequence. We extend this definition to a subset of words of length n, ...

A de Bruijn sequence over a finite alphabet of span n is a cyclic string such that all words of length n appear exactly once as factors of this sequence. We extend this definition to a subset of words of length n, ...

We give a complete proof of the following theorem: Every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n+1. Every de Bruijn sequence of order n in two symbols can ...

Let G = (V, A) be an Eulerian directed graph with an arc-labeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that ...

Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the ...

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions ...

In this work we present a version of the so called Chen and Chv´atal’s conjecture for directed graphs. A line of a directed graph D is defined by an ordered pair (u, v), with u and v two distinct vertices of D, as the ...