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Periods in Extensions of Words

Tero Harju, Dirk Nowotka, Periods in Extensions of Words. TUCS Technical Reports 736, Turku Centre for Computer Science, 2006.

Abstract:

Let <i>z</i> be a prefix of <i>w</i>.
If <i>wz</i> and <i>w</i> have the same period then
<i>|u| < per(w)- gcd(|w|,|z|)</i> where <i>per(w)</i> denotes
the smallest period of <i>w</i>.
More detailed improvements of this result are proven.
As a corollary a short proof is given of the fact that
if <i>u,v,w</i> are primitive such that <i>u</i> is a prefix of <i>v</i>,
and <i>v</i> is a prefix of <i>w</i>, then <i>|w| > 2|u|</i>.

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BibTeX entry:

@TECHREPORT{tHaNo06a,
  title = {Periods in Extensions of Words},
  author = {Harju, Tero and Nowotka, Dirk},
  number = {736},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2006},
  ISBN = {952-12-1661-1},
}

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

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