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

Unique subwords in nonperiodic words


Author: C. M. Weinbaum
Journal: Proc. Amer. Math. Soc. 109 (1990), 615-619
MSC: Primary 20M05; Secondary 05A05, 20F05
MathSciNet review: 1017852
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A,D$ be words over some alphabet. $ D$ has position $ p$ in the cyclic word $ A$ if the cyclic permutation of $ A$ which begins with the $ p$th letter of $ A$ has an initial subword equal to $ D$. It is proved that every nonperiodic word $ A$ of length $ > 1$ has a cyclic permutation which is a product BC for some nonempty subwords $ B,C$ having unique positions in the cyclic word $ A$.


References [Enhancements On Off] (What's this?)

  • [1] W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1017852-0
PII: S 0002-9939(1990)1017852-0
Keywords: Generators and relations, presentations, cancellation theory, word problems, free semigroups, partitions
Article copyright: © Copyright 1990 American Mathematical Society