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Weinbaum Factorizations of Primitive Words

Volker Diekert, Tero Harju, Dirk Nowotka, Weinbaum Factorizations of Primitive Words. TUCS Technical Reports 780, Turku Centre for Computer Science, 2006.

Abstract:

C.M. Weinbaum 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.

Files:

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BibTeX entry:

@TECHREPORT{tDiHaNo06a,
  title = {Weinbaum Factorizations of Primitive Words},
  author = {Diekert, Volker and Harju, Tero and Nowotka, Dirk},
  number = {780},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2006},
  ISBN = {952-12-1774-X},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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