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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Weinbaum's conjecture on unique subwords of nonperiodic words

Authors: Andrew J. Duncan and James Howie
Journal: Proc. Amer. Math. Soc. 115 (1992), 947-954
MSC: Primary 20F05; Secondary 20F10
MathSciNet review: 1110541
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Abstract: Following a conjecture of Weinbaum, we show that every nonperiodic word $ W$ of length at least 2 in a free group has a cyclic permutation of the form UV, where each of $ U$ and $ V$ occur precisely once as a cyclic subword of $ W$ and neither occurs as a cyclic subword of $ {W^{ - 1}}$. In fact, we prove a somewhat stronger version of this result and also give a number of applications to one-relator products of groups.

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PII: S 0002-9939(1992)1110541-5
Article copyright: © Copyright 1992 American Mathematical Society