Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T07:53:44.952Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Conjecture by Eriksson Concerning Overlap in Strings

Published online by Cambridge University Press:  01 September 1999

ISA CAKIR ,
OURANIA CHRYSSAPHINOU  and
MARIANNE MÅNSSON
ISA CAKIR
Affiliation:
Abteilung für Angewandte Mathematik, Universität Zürich-Irchel, Winterthurerstrasse 190, CH 8057 Zürich, Switzerland (e-mail: isa.cakir@winterthur.ch)
OURANIA CHRYSSAPHINOU
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, GR 157 84 Athens, Greece (e-mail ocrysaf@atlas.uoa.gr)
MARIANNE MÅNSSON
Affiliation:
Department of Mathematics, Chalmers University of Technology, S 412 96 Göteborg, Sweden (e-mail marianne@math.chalmers.se)
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a finite alphabet Ω and strings consisting of elements from Ω. For a given string w, let cor(w) denote the autocorrelation, which can be seen as a measure of the amount of overlap in w. Furthermore, let aw(n) be the number of strings of length n that do not contain w as a substring. Eriksson [4] stated the following conjecture: if cor(w)>cor(w′), thenaw(n)>aw′(n) from the first n where equality no longer holds. We prove that this is true if [mid ]Ω[mid ][ges ]3, by giving a lower bound for aw(n)−aw′(n).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 5 , September 1999 , pp. 429 - 440
Copyright
1999 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.)