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Periodicity and Unbordered Factors of Words

Dirk Nowotka, Periodicity and Unbordered Factors of Words. TUCS Dissertations 50. Turku Centre for Computer Science, 2004.


Several questions about relationships between borders and global and local periods of finite words are investigated in this thesis. We consider the density of critical points and applications of the critical factorization theorem. A relationship between unbordered conjugates and internal critical points is established and a border correlation function of words is investigated. Moreover, we study the relation between the global period and the length of the longest unbordered factor of a word. In particular, we resolve a longstanding conjecture called the sharpened DuvalХs conjecture.

BibTeX entry:

  title = {Periodicity and Unbordered Factors of Words},
  author = {Nowotka, Dirk},
  number = {50},
  series = {TUCS Dissertations},
  school = {Turku Centre for Computer Science},
  year = {2004},
  keywords = {combinatorics on words, repetition, border, periodicity, critical factorization, border correlation, Duval's conjecture},
  ISBN = {952-12-1361-2},

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