J. Cassaigne, S. Ferenczi and L. Zamboni, Imbalances in Arnoux-Rauzy Sequences. Ann. Inst. Fourier. To appear. Home/Search Document Not in Database Summary Related Articles Check |
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Recent Results on Extensions of Sturmian Words - Berstel (2001) (2 citations) (Correct)
....a rotation was given by Rauzy in 1982 for the Tribonacci word [40] and they are known for large families of other AR words. It was believed that every ternary AR word codes the orbit of a point under a rotation on T . However, this does not hold, as proved by Cassaigne, Ferenczi and Zamboni [12]. They prove the proposition below, and then use another result by Rauzy to get the negative answer. Proposition 3.3 There exist AR words x that are imbalanced, in the following sense. For each integer n, there are factors u; v of x equal length with jjuj a jvj a j n for some letter a. It can ....
J. Cassaigne, S. Ferenczi, and L. Q. Zamboni. Imbalances in Arnoux-Rauzy sequences. Ann. Inst. Fourier. to appear.
Generalized balances in Sturmian words - Fagnot, Vuillon (2000) (2 citations) (Correct)
.... Email: fagnot univ mlv.fr y LIAFA Universit e Paris 7, 2, place Jussieu, Case 7014, 75251 Paris Cedex 05, France, Email: Laurent.Vuillon liafa.jussieu.fr 1 Generalized balances in Sturmian words 2 (Gaujal [8] Mairesse and Vuillon [14] Recently, a paper of Cassaigne, Ferenczi and Zamboni [6] illustrates how the presence of balances is intimately connected with the underlying geometry: an Arnoux Rauzy sequence which is totally unbalanced in the sense of Cassaigne Ferenczi Zamboni cannot be a natural coding of a rotation on a torus. Berth e and Tijdeman [4] consider balance in ....
J. Cassaigne, S. Ferenczi and L. Zamboni, Imbalances in Arnoux-Rauzy Sequences. Ann. Inst. Fourier. To appear.
Generalized balances in Sturmian words - Fagnot, Vuillon (2000) (2 citations) (Correct)
.... the paper of Cassaigne, Ferenczi and Zamboni illustrates how the presence of balances is intimately connected with the underlying geometry: an Arnoux Rauzy sequence which is totally unbalanced in the sense of Cassaigne Ferenczi Zamboni cannot be a natural coding of a rotation on a torus (see [5]) A way to extend the balance property is to consider the number of occurrences of a word u in w (denoted by jwj u ) and in w 0 : The difference of the numbers of occurrences is studied and the following main theorem is shown (Theorem 11) Theorem Let x be a Sturmian word. Let u, w and w 0 ....
J. Cassaigne, S. Ferenczi and L. Zamboni, Imbalances in Arnoux-Rauzy Sequences. Preprint IML 2000.
Structure Of Three-Interval Exchange Transformations I.. - Ferenczi, Holton.. (2001) (2 citations) Self-citation (Ferenczi Zamboni) (Correct)
.... is very satisfying in the special case of the so called Tribonacci system, as pioneered by work of Arnoux and Rauzy [3, 5, 35] a more general canonical equivalence (through what is called a natural coding) between two dimensional rotations and Arnoux Rauzy sequences is not always verified (see [12]) Berthe and Vuillon [7] studied the dynamics resulting from two rotations on the circle (see also work of Arnoux, Berthe and Ito in [4] They found in this case the symbolic counterpart is given by a family of Z 2 shifts, and that the Jacobi Perron algorithm provides a suitable arithmetic ....
J. CASSAIGNE, S. FERENCZI, L.Q. ZAMBONI, Imbalances in Arnoux-Rauzy sequences, preprint, Ann. Inst. Fourier, 50 (2000), p. 1265--1276.
Generalized balances in Sturmian words - Fagnot, Vuillon (2000) (2 citations) (Correct)
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J. Cassaigne, S. Ferenczi and L. Zamboni, Imbalances in Arnoux-Rauzy Sequences. Ann. Inst. Fourier. To appear.
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