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On the positivity set of a linear recurrence sequence

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada, V5A 1S6

    Jason P. Bell

  2. Christian Doppler Laboratory for Portfolio Risk Management, Vienna University of Technology, Wiedner Hauptstraße, 8-10/105-1, Austria

    Stefan Gerhold

Authors
  1. Jason P. Bell
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  2. Stefan Gerhold
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Additional information

Supported in part by the Christian Doppler Research Association (CDG). S. Gerhold gratefully acknowledges a fruitful collaboration and continued support by Bank Austria and OBFA through CDG. Supported in part by the FWF grant F1305.

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Bell, J.P., Gerhold, S. On the positivity set of a linear recurrence sequence. Isr. J. Math. 157, 333–345 (2007). https://doi.org/10.1007/s11856-006-0015-1

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  • DOI: https://doi.org/10.1007/s11856-006-0015-1

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