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Words without Near-Repetitions

Published online by Cambridge University Press:  20 November 2018

J. Currie  and
A. Bendor-Samuel
J. Currie
Affiliation:
Department of Mathematics University of Winnipeg Winnipeg, Manitoba R3B 2E9
A. Bendor-Samuel
Affiliation:
Department of Mathematics University of Winnipeg Winnipeg, Manitoba R3B 2E9
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Abstract

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We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.

Keywords

68Q03C.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 161 - 166
Copyright
Copyright © Canadian Mathematical Society 1992 

Footnotes

The research of the first author was supported by an NSERC Operating Grant.

The second author was supported by an NSERC Undergraduate Summer Research Award.

References

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