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Autocorrelation and the Enumeration of Strings Avoiding a Fixed String

Published online by Cambridge University Press:  01 March 1997

Stockholm University, S-106 09 Stockholm, Sweden (e-mail:


Considering strings over a finite alphabet [Ascr ], say that a string is w-avoiding if it does not contain w as a substring. It is known that the number aw(n) of w-avoiding strings of length n depends only on the autocorrelation of w as defined by Guibas–Odlyzko. We give a simple criterion on the autocorrelations of w and w′ for determining whether aw(n) > aw(n) for all large enough n.

Research Article
1997 Cambridge University Press

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