Francesca Fiorenzi

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A vertex colouring of a graph G is nonrepetitive if for any path P = (v1, v2, . . . , v2r) in G, the first half is coloured differently from the second half. The Thue choice number of G is the least integer l such that for every l-list assignment L of G, there exists a nonrepetitive L-colouring of G. We prove that for any positive integer l, there is a tree(More)
We define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the shifts. We prove that these classes define invariants shift equivalence(More)
We study the sofic tree shifts of A ∗ , where Σ∗ is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if X ⊂ A ∗ is a sofic tree shift, then the configurations in X whose orbit under the shift action is finite are dense in X , and, as a consequence of this, we deduce(More)