The Positivity Set of a Recurrence Sequence

Details The Positivity Set of a Recurrence Sequence The Positivity Set of a Recurrence Sequence

2005-06-20

arxiv.org/abs/math/0506398v1

Mathematics

Combinatorics

Scientific paper

We consider real sequences $(f_n)$ 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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