Israel Journal of Mathematics

, Volume 157, Issue 1, pp 333–345 | Cite as

On the positivity set of a linear recurrence sequence

  • Jason P. Bell
  • Stefan Gerhold


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.


Rational Number Characteristic Root Real Sequence Positive Density Linear Recurrence 
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Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  • Jason P. Bell
    • 1
  • Stefan Gerhold
    • 2
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Christian Doppler Laboratory for Portfolio Risk ManagementVienna University of TechnologyWiedner HauptstraßeAustria

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