Secuencias recurrentes lineales de quinto orden y su positividad
Palabras clave:
Problema de positividad, secuencia recurrente, decidibilidad
Resumen
Considere una secuencia de recurrencia lineal de quinto orden con coeficientes enteros. Se muestra que el problema de si cada uno de sus elementos es no negativo es decidible.
Citas
Baker, A. and Wüstholz, G.; Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19--62.
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.
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.
Publicado
2018-06-24
Cómo citar
Laohakosol, V., & Tangsupphathawat, P. (2018). Secuencias recurrentes lineales de quinto orden y su positividad. Divulgaciones Matemáticas, 19(1), 1-19. Recuperado a partir de https://www.produccioncientificaluz.org/index.php/divulgaciones/article/view/36557
Sección
Artículos de Investigación
