A1 Refereed original research article in a scientific journal
Periods in extensions of words
Authors: Harju T, Nowotka D
Publisher: SPRINGER
Publication year: 2006
Journal:: Acta Informatica
Journal name in source: ACTA INFORMATICA
Journal acronym: ACTA INFORM
Volume: 43
Issue: 3
First page : 165
Last page: 171
Number of pages: 7
ISSN: 0001-5903
DOI: https://doi.org/10.1007/s00236-006-0014-z
Abstract
Let pi(w) denote the minimum period of the word w,let w be a primitive word with period pi(w) < |w|, and let z be a prefix of w. It is shown that if pi(wz) = pi(w), then |z| < pi(w) - gcd (|w|, |z|). Detailed improvements of this result are also proven. Finally, we show that each primitive word w has a conjugate w' = vu, where w = uv, such that pi(w') = |w'| and |u| < pi(w). As a corollary we give a short proof of the fact that if u,v,w are words such that u(2) is a prefix of v(2), and v(2) is a prefix of w(2), and v is primitive, then |w| > 2|u|.
Let pi(w) denote the minimum period of the word w,let w be a primitive word with period pi(w) < |w|, and let z be a prefix of w. It is shown that if pi(wz) = pi(w), then |z| < pi(w) - gcd (|w|, |z|). Detailed improvements of this result are also proven. Finally, we show that each primitive word w has a conjugate w' = vu, where w = uv, such that pi(w') = |w'| and |u| < pi(w). As a corollary we give a short proof of the fact that if u,v,w are words such that u(2) is a prefix of v(2), and v(2) is a prefix of w(2), and v is primitive, then |w| > 2|u|.
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