A generalization of Sturmian sequences: Combinatorial structure and transcendence
A generalization of the self-dual induction to every interval exchange transformation
We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic...
A generator of morphisms for infinite words
We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne's thesis are 2-avoidable. We also prove that there exist exponentially many -free ternary words and -free 4-ary words. Finally we give small morphisms for binary words containing only the squares 2, 12 and (01)² and for binary words avoiding...
A graph approach to computing nondeterminacy in substitutional dynamical systems
We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems.
A graph method for Markov models solving
A Hajós type result on factoring finite abelian groups by subsets. II
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.
A hierarchy for circular codes
We first prove an extremal property of the infinite Fibonacci* word f: the family of the palindromic prefixes {hn | n ≥ 6} of f is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones.
A Hierarchy of Automatic ω-Words having a Decidable MSO Theory
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSO-interpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above...
A Left-First Search Algorithm for Planar Graphs.
A length bound for binary equality words
Let be an equality word of two binary non-periodic morphisms with unique overflows. It is known that if contains at least 25 occurrences of each of the letters and , then it has to have one of the following special forms: up to the exchange of the letters and either , or with . We will generalize the result, justify this bound and prove that it can be lowered to nine occurrences of each of the letters and .
A linear algorithm for bend-optimal orthogonal drawings of triconnected cubic plane graphs.
A little more about morphic Sturmian words
Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial...
A logical model of HCP.
A Loopless Implementation of a Gray Code for Signed Permutations
A lower bound for the arithmetical complexity of Sturmian words.
A morphic approach to combinatorial games : the Tribonacci case
We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.
A morphic approach to combinatorial games: the Tribonacci case
We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.
A multilevel algorithm for force-directed graph-drawing.
A multilevel algorithm for the minimum 2-sum problem.
A new algorithm for finding minimal cycle-breaking sets of turns in a graph.