Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T06:59:54.288Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)