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Positivity of Second Order Linear Recurrent Sequences

Vesa Halava, Tero Harju, Mika Hirvensalo, Positivity of Second Order Linear Recurrent Sequences. TUCS Technical Reports 685, Turku Centre for Computer Science, 2005.

Abstract:

We prove that the following problem, which is called the
Positivity Problem in the literature, is algorithmically solvable:
Given a sequence $(u_n)_{n=0}^\infty$ of integers satisfying a linear second order recurrence relation, determine whether or not $u_n$ is
non-negative for all $n$. This problem has connection to other
fields of mathematics through the theory of matrices.

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BibTeX entry:

@TECHREPORT{tHaHaHi05a,
  title = {Positivity of Second Order Linear Recurrent Sequences},
  author = {Halava, Vesa and Harju, Tero and Hirvensalo, Mika},
  number = {685},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2005},
  keywords = {integer sequence; second order; homogeneous linear recurrence relation; positivity},
  ISBN = {952-12-1541-0},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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