Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22128
Cakir, I; Chryssaphinou, O; Månsson, M (1999). On a conjecture by Eriksson concerning overlap in strings. Combinatorics, Probability & Computing, 8(5):429-440.
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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  stated the following conjecture: if cor(w)>cor(w′), then aw(n)>aw′(n) from the first n where equality no longer holds. We prove that this is true if [mid R:]Ω[mid R:][gt-or-equal, slanted]3, by giving a lower bound for aw(n)−aw′(n).
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Deposited On:||29 Nov 2010 16:27|
|Last Modified:||14 Dec 2013 17:37|
|Publisher:||Cambridge University Press|
|Additional Information:||Copyright: Cambridge University Press|
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