I. Fagnot and L. Vuillon,Generalized balances in Sturmian words, prepublication LIAFA 2000/02. Home/Search Document Details and Download
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Recent Results on Extensions of Sturmian Words - Berstel (2001) (2 citations) (Correct)
....of this theorem that deserve to be mentioned. The rst concerns balance. Instead of considering the number juj a of occurrences of a letter a in a word u, one may compute more generally the number juj z of occurrences of the word z as a factor in u. It has been shown by Fagnot and Vuillon [27] that this extended notion also characterizes Sturmian words in the following sense. Theorem 2.7 An in nite word x is Sturmian if and only if, for each pairs of factors u, v of equal length jjuj z jvj z j jzj for all nonempty words z. 2.3 Factor graph One of the basic tools for ....
I. Fagnot and L. Vuillon. Generalized balance in Sturmian words. Technical Report 2000-02, Liafa, 2000.
Periodicity and Almost-periodicity - Tijdeman (2002) (Correct)
....rational. The Fraenkel conjecture has been proved in case n = 3 by Morikawa [33] cf. 53] in case n = 4 by Altman, Gaujal, and Hordijk [1] and in case n = 5; 6 by the author [56] Related results have been obtained by a.o. Fraenkel, Morikawa, and Simpson, cf. 57] Recently Fagnot and Vuillon [19] have studied balancedness with respect to subwords of given length instead of letters. 7 Sti words Another way to measure the regularity of a word is to compute its complexity. For n = 1; 2; the complexity P (n) of a word is de ned as the number of 6 distinct subwords of length n. In ....
Fagnot I. and Vuillon L., Generalized balances in sturmian words, Discr. Appl. Math. 121 (2002), 83-101.
Return Words In Sturmian And Episturmian Words - Justin, Vuillon (2000) (2 citations) Self-citation (Vuillon) (Correct)
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I. Fagnot and L. Vuillon,Generalized balances in Sturmian words, prepublication LIAFA 2000/02.
Return Words In Sturmian And Episturmian Words - Justin, Vuillon (2000) (2 citations) Self-citation (Vuillon) (Correct)
.... fractions and a main argument is to show, using return words, that arbitrarily long prefixes are almost squares (see [1] Fagnot and Vuillon give a generalization of the notion of balance property for Sturmian words and the proof is based on return words and combinatorics on words (see [10]) Cassaigne also uses this tool to investigate a Rauzy conjecture (see [4] At last, the second author shows that a sequence is Sturmian if and only if for each word w appearing in the sequence, the number of return words of w is exactly two (see [14] Recall that Sturmian sequences are ....
I. Fagnot and L. Vuillon,Generalized balances in Sturmian words, prepublication LIAFA 2000/02.
Return Words In Sturmian And Episturmian Words - Justin, Vuillon (2000) (2 citations) Self-citation (Vuillon) (Correct)
.... fractions and a main argument is to show, using return words, that arbitrarily long prefixes are almost squares (see [1] Fagnot and Vuillon give a generalization of the notion of balance property for Sturmian words and the proof is based on return words and combinatorics on words (see [9]) Cassaigne also uses this tool to investigate a Rauzy conjecture (see [4] At last, the second author shows that a sequence is Sturmian if and only if for each word w appearing in the sequence, the number of return words of w is exactly two (see [14] Recall that Sturmian sequences are ....
I. Fagnot and L. Vuillon,Generalized balances in Sturmian words, prepublication LIAFA 2000/02.
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