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Some kinds of primitive and non-primitive words.
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- Author(s): Chunhua, Cao; Shuang, Yang; Di, Yang
- Source:
Acta Informatica. Sep2014, Vol. 51 Issue 6, p339-346. 8p. - Source:
- Additional Information
- Subject Terms:
- Abstract: If the length of a primitive word $$p$$ is equal to the length of another primitive word $$q$$ , then $$p^{n}q^{m}$$ is a primitive word for any $$n,m\ge 1$$ and $$(n,m)\ne (1,1)$$ . This was obtained separately by Tetsuo Moriya in 2008 and Shyr and Yu in 1994. In this paper, we prove that if the length of $$p$$ is divisible by the length of $$q$$ and the length of $$p$$ is less than or equal to $$m$$ times the length of $$q$$ , then $$p^{n}q^{m}$$ is a primitive word for any $$n,m\ge 1$$ and $$(n,m)\ne (1,1)$$ . Then we show that if $$uv,u$$ are non-primitive words and the length of $$u$$ is divisible by the length $$v$$ or one of the length of $$u$$ and $$uv$$ is odd for any two nonempty words $$u$$ and $$v$$ , then $$u$$ is a power of $$v$$ . [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of Acta Informatica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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