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Pattern Avoidance and Overlap in Strings

Published online by Cambridge University Press:  06 September 2002

MARIANNE MÅNSSON
MARIANNE MÅNSSON
Affiliation:
Department of Mathematics, Chalmers University of Technology, SE 412 96 Göteborg, Sweden (e-mail: [email protected])
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Abstract

Consider a finite alphabet Ω and patterns which consist of characters from Ω. For a given pattern w, let cor(w) denote its autocorrelation, which can be seen as a measure of the amount of overlap in w. Letting aw(n) denote the number of strings over Ω of length n which do not contain w as a substring, the main result of this paper is: If cor(w) > cor(w′) then aw(n)−aw′(n) > (|Ω|−1)(aw(n−1)−aw′(n−1)) for n [ges ] N, and the value of N is given. This result confirms a conjecture by Eriksson [2], which was previously proved to be true by Cakir, Chryssaphinou and Månsson [1] when |Ω| [ges ] 3.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 4 , July 2002 , pp. 393 - 402
Copyright
2002 Cambridge University Press

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