Periods in extensions of words

: Harju T, Nowotka D

Publisher: SPRINGER

: 2006

Acta Informatica

ACTA INFORMATICA

: ACTA INFORM

: 43

: 3

: 165

: 171

: 7

: 0001-5903

DOI: https://doi.org/10.1007/s00236-006-0014-z

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|.

Mathematics