Weinbaum factorizations of primitive words

Diekert, Volker, Harju, Tero and Nowotka, Dirk (2010) Weinbaum factorizations of primitive words Russian Mathematics, 54 (1). pp. 16-25. DOI 10.3103/S1066369X10010032.

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Abstract

C. M. Weinbaum [Proc. AMS, 109(3):615-619, 1990] showed the following: Let w be a primitive word and a be letter in w. Then a conjugate of w can be written as uv such that a is a prefix and a suffix of u, but v neither starts nor ends with a, and u and v have a unique position in w as cyclic factors. The latter condition means that there is exactly one conjugate of w having u as a prefix and there is exactly one conjugate of w having v as a prefix. It is this condition which makes the result non-trivial.

We give a simplified proof for Weinbaum's result. Guided by this proof we exhibit quite different, but still simple, proofs for more general statements. For this purpose we introduce the notion of Weinbaum factor and Weinbaum factorization.

Document Type: Article
Keywords: combinatorics on words conjugates Weinbaum factorizations
Research affiliation: ?? dep_sys ??
Refereed: Yes
DOI etc.: 10.3103/S1066369X10010032
ISSN: 1066-369X
Date Deposited: 01 Feb 2013 17:00
Last Modified: 01 Feb 2013 17:00
URI: http://eprints.uni-kiel.de/id/eprint/20236

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