Periods in Extensions of Words.

Harju, Tero and Nowotka, Dirk (2006) Periods in Extensions of Words. Acta Informatica, 43 (3). pp. 165-171. DOI 10.1007/s00236-006-0014-z.

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Abstract

Let p(w) denote the minimum period of the word w, let w be a primitive word with period p(w)<|w|, and let z be a prefix of w. It is shown that if p(wz)=p(w), then |z|<p(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 p(w')=|w'| and |u|<p(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|.

Document Type: Article
Keywords: combinatorics on words periods
Research affiliation: Kiel University
Refereed: Yes
Date Deposited: 12 Feb 2013 17:11
Last Modified: 23 Sep 2019 20:01
URI: https://oceanrep.geomar.de/id/eprint/20284

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