A1 Refereed original research article in a scientific journal
About Duval's conjecture
Authors: Harju T, Nowotka D
Publication year: 2003
Journal:: Lecture Notes in Computer Science
Journal name in source: DEVELOPMENTS IN LANGUAGE THEORY, PROCEEDINGS
Journal acronym: LECT NOTES COMPUT SC
Volume: 2710
First page : 316
Last page: 324
Number of pages: 9
ISBN: 3-540-40434-1
ISSN: 0302-9743
Abstract
A word is called unbordered if it has no proper prefix which is also a suffix of that word. Let mu(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix equal to mu(w) be called Duval extension. A Duval extension is called trivial, if its longest unbordered factor is of the length of the period of that Duval extension. In 1982 it was shown by Duval that every Duval extension w longer than 3mu(w)-4 is trivial. We improve that bound to 5mu(w)/2-1 in this paper, and with that, move closer to the bound 2mu(w) conjectured by Duval. Our proof also contains a natural application of the Critical Factorization Theorem.
A word is called unbordered if it has no proper prefix which is also a suffix of that word. Let mu(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix equal to mu(w) be called Duval extension. A Duval extension is called trivial, if its longest unbordered factor is of the length of the period of that Duval extension. In 1982 it was shown by Duval that every Duval extension w longer than 3mu(w)-4 is trivial. We improve that bound to 5mu(w)/2-1 in this paper, and with that, move closer to the bound 2mu(w) conjectured by Duval. Our proof also contains a natural application of the Critical Factorization Theorem.
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