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Morphically primitive words

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journal contribution
posted on 29.04.2009, 12:45 by Daniel Reidenbach, Johannes C. Schneider
In the present paper, we introduce an alternative notion of the primitivity of words, that–unlike the standard understanding of this term–is not based on the power (and, hence, the concatenation) of words, but on morphisms. For any alphabet Σ, we call a word wΣ* morphically imprimitive provided that there are a shorter word v and morphisms h,h′:Σ*→Σ* satisfying h(v)=w and h′(w)=v, and we say that w is morphically primitive otherwise. We explain why this is a well-chosen terminology, we demonstrate that morphic (im-) primitivity of words is a vital attribute in many combinatorial domains based on finite words and morphisms, and we study a number of fundamental properties of the concepts under consideration.

History

School

  • Science

Department

  • Computer Science

Citation

REIDENBACH, D. and SCHNEIDER, J.C., 2009. Morphically primitive words. Theoretical Computer Science, 140 (21-23), pp. 2148-2161

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publication date

2009

Notes

This article was published in the journal, Theoretical Computer Science [© Elsevier]. The definitive version is available at: http://www.elsevier.com/wps/find/journaldescription.cws_home/505625/description#description

ISSN

0304-3975

Language

en

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