A Note on a Conjecture of Duval and Sturmian Words
نویسندگان
چکیده
منابع مشابه
A Note on a Conjecture of Duval and Sturmian Words
We prove a long standing conjecture of Duval in the special case of Sturmian words. Mathematics Subject Classification. 68R15, 37B10. Let U be a nonempty word on a finite alphabet A. A nonempty word B different from U is called a border of U if B is both a prefix and suffix of U. We say U is bordered if U admits a border, otherwise U is said to be unbordered. For example, U = 011001011 is borde...
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Dejean conjectured that the repetition threshold of a k-letter alphabet is k/(k−1), k = 3, 4. Values of the repetition threshold for k < 5 were found by Thue, Dejean and Pansiot. Moulin-Ollagnier attacked Dejean’s conjecture for 5 ≤ k ≤ 11. Building on the work of Moulin-Ollagnier, we propose a method for deciding whether a given Sturmian word with quadratic slope confirms the conjecture for a ...
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The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. A word is bordered, if it has a proper prefix that is also a suffix of that word. Consider a finite word w of length n. Let μ(w) denote the maximum length of its unbordered factors, and let ∂(w) denote the period of w. Clearly, μ(w) ≤ ∂(w). We establish that μ(w) = ∂(w),...
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The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 2002
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita:2002001