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Minimal Duval Extensions

Tero Harju, Dirk Nowotka, Minimal Duval Extensions. TUCS Technical Reports 520, Turku Centre for Computer Science, 2003.

Abstract:

A word <i>v</i> = <i>wu</i> is a (nontrivial) Duval extension
of the unbordered word <i>w</i>, if (<i>u</i> is not a prefix
of <i>v</i> and) <i>w</i> is an unbordered factor of <i>v</i>
of maximum length. After a short survey of the research topic
related to Duval extensions, we show that, if <i>wu</i> is
a minimal Duval extension of <i>w</i>, then <i>u</i> is a factor
of <i>w</i>. We also show that finite, unbordered factors
of Sturmian words are Lyndon words.

Files:

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BibTeX entry:

@TECHREPORT{tHaNo03a,
  title = {Minimal Duval Extensions},
  author = {Harju, Tero and Nowotka, Dirk},
  number = {520},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2003},
  keywords = {combinatorics on words, periodicity, unbordered factors, Duval's conjecture, Sturmian words, Lyndon words},
  ISBN = {952-12-1149-0},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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