138 research outputs found
The Positivity Set of a Recurrence Sequence
We consider real sequences that satisfy a linear recurrence with
constant coefficients. We show that the density of the positivity set of such a
sequence always exists. In the special case where the sequence has no positive
dominating characteristic root, we establish that the density is positive.
Furthermore, we determine the values that can occur as density of such a
positivity set, both for the special case just mentioned and in general
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