Fifth order linear recurrence sequences and their positivity
Keywords:
Positivity problem, recurrence sequences, decidability
Abstract
Consider a fifth order linear recurrence sequence with integer coeficients. The problem whether each of its elements is nonnegative is shown to be decidable.
References
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Halava, V.; Harju, T. and Hirvensalo, M.; Positivity of second order linear recurrent sequences, Discrete Appl. Math., 154 (2006), 447--451.
Laohakosol, V. and Tangsupphathawat, P.; Positivity of third order linear recurrence sequences, Discrete Appl. Math. 157 (2009), 3239--3248.
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Laohakosol, V.; Tangsupphathawat, P. and Dangskul, S.; Values taken by linear combinations of cosine functions, Appl. Math. E-Notes, 10 (2011), 184--190.
Ouaknine, J. and Worrell, J.; Decision problems for linear recurrence sequences, Lecture Notes in Computer, Springer, Berlin-heidelberg, 7550 (2012), 21--28.
Tangsupphathawat, P.; Punnim, N. and Laohakosol, V.; The positivity problem for fourth order linear recurrence sequences is decidable, Colloq. Math. 128 (2012), 133--142.
Tangsupphathawat, P.; Punnim, N. and Laohakosol, V.; Another proof of the positivity problem for fourth order recurrence sequences, East-West J. Math. 14 (2012), 185--200.
Bell, J. P. and Gerhold, S.; On the positivity set of a linear recurrence sequence, Israel J. Math., 157 (2007), 333--345.
Burke, J. R. and Webb, W. A.; Asymptotic behaviour of linear recurrences, Fibonacci Quarterly, 19 (1981), 318--321.
Cassels, J. W. S.; An Introduction to Diophantine Approximation, Cambridge University Press, 1957.
Halava, V.; Harju, T.; Hirvensalo, M. and Karhumäki, J.; Skolem's problem - On the border between decidability and undecidability, TUCS
Technical Report, No. 683, April 2005, Turku Centre for Computer Science, 36 pp.
Halava, V.; Harju, T. and Hirvensalo, M.; Positivity of second order linear recurrent sequences, Discrete Appl. Math., 154 (2006), 447--451.
Laohakosol, V. and Tangsupphathawat, P.; Positivity of third order linear recurrence sequences, Discrete Appl. Math. 157 (2009), 3239--3248.
Laohakosol, V. and Tangsupphathawat, P.; A remark about the positivity problem of fourth order linear recurrence sequences, Acta et Commentationes Universitatis Tartuensis de Mathematica 18 (2014), 3--8.
Laohakosol, V.; Tangsupphathawat, P. and Dangskul, S.; Values taken by linear combinations of cosine functions, Appl. Math. E-Notes, 10 (2011), 184--190.
Ouaknine, J. and Worrell, J.; Decision problems for linear recurrence sequences, Lecture Notes in Computer, Springer, Berlin-heidelberg, 7550 (2012), 21--28.
Tangsupphathawat, P.; Punnim, N. and Laohakosol, V.; The positivity problem for fourth order linear recurrence sequences is decidable, Colloq. Math. 128 (2012), 133--142.
Tangsupphathawat, P.; Punnim, N. and Laohakosol, V.; Another proof of the positivity problem for fourth order recurrence sequences, East-West J. Math. 14 (2012), 185--200.
Published
2018-06-24
How to Cite
Laohakosol, V., & Tangsupphathawat, P. (2018). Fifth order linear recurrence sequences and their positivity. Divulgaciones Matemáticas, 19(1), 1-19. Retrieved from https://www.produccioncientificaluz.org/index.php/divulgaciones/article/view/36557
Section
Research papers
