A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Periods in extensions of words
Tekijät: Harju T, Nowotka D
Kustantaja: SPRINGER
Julkaisuvuosi: 2006
Lehti:: Acta Informatica
Tietokannassa oleva lehden nimi: ACTA INFORMATICA
Lehden akronyymi: ACTA INFORM
Vuosikerta: 43
Numero: 3
Aloitussivu: 165
Lopetussivu: 171
Sivujen määrä: 7
ISSN: 0001-5903
DOI: https://doi.org/10.1007/s00236-006-0014-z
Tiivistelmä
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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