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).