Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-20T17:35:37.381Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Adian, S. I., The Burnside Problem and Identities in Groups, Springer-Verlag, New York 1979.Google Scholar
2. Arshon, S., Demonstration de Vexistence des suites asymétriques infinies, Mat. Sb. 2 (44) (1937), 769–779.Google Scholar
3. Brown, T. C., Is there a sequence on four symbols in which no two adjacent segments are permutations of each other?, Amer. Math. Monthly 78(1971), 886–888.Google Scholar
4. Edmunds, C., personal communication.Google Scholar
5. Novikov, P. S. and Adjan, S. I., Infinite periodic groups I, II, III, Math. U.S.S.R. Izv. 2(1968) I: 209-236, II: 241-479,111:665-685.Google Scholar
6. Thue, A., UberunendlicheZeichenreihen,Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana (1912), 1-67.Google Scholar