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Title: Morphically primitive words
Authors: Reidenbach, Daniel
Schneider, Johannes C.
Keywords: Combinatorics on words
Primitivity
Morphisms
Fixed points
Issue Date: 2009
Publisher: © Elsevier
Citation: REIDENBACH, D. and SCHNEIDER, J.C., 2009. Morphically primitive words. Theoretical Computer Science, 140 (21-23), pp. 2148-2161
Abstract: 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.
Description: 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
Version: Accepted for publication
DOI: 10.1016/j.tcs.2009.01.020
URI: https://dspace.lboro.ac.uk/2134/4561
ISSN: 0304-3975
Appears in Collections:Published Articles (Computer Science)

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