On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence
Abstract Recently, Bednarz introduced a new two-parameter generalization of the Fibonacci sequence, which is called the ( k , p ) $(k,p)$ -Fibonacci sequence and denoted by ( F k , p ( n ) ) n ≥ 0 $(F_{k,p}(n))_{n\geq0}$ . In this paper, we study the geometry of roots of the characteristic polynomia...
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2021-01-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-020-03186-8 |
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doaj-9b5b4284fe6b4c458ddc924c47f5f5602021-01-10T12:52:46ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-01202111910.1186/s13662-020-03186-8On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequencePavel Trojovský0Department of Mathematics, Faculty of Science, University of Hradec KraloveAbstract Recently, Bednarz introduced a new two-parameter generalization of the Fibonacci sequence, which is called the ( k , p ) $(k,p)$ -Fibonacci sequence and denoted by ( F k , p ( n ) ) n ≥ 0 $(F_{k,p}(n))_{n\geq0}$ . In this paper, we study the geometry of roots of the characteristic polynomial of this sequence.https://doi.org/10.1186/s13662-020-03186-8Generalized Fibonacci sequenceCharacteristic polynomialEneström–Kakeya theoremDescartes’ sign rule |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Pavel Trojovský |
| spellingShingle |
Pavel Trojovský On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence Advances in Difference Equations Generalized Fibonacci sequence Characteristic polynomial Eneström–Kakeya theorem Descartes’ sign rule |
| author_facet |
Pavel Trojovský |
| author_sort |
Pavel Trojovský |
| title |
On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence |
| title_short |
On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence |
| title_full |
On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence |
| title_fullStr |
On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence |
| title_full_unstemmed |
On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence |
| title_sort |
on the characteristic polynomial of ( k , p ) $(k,p)$ -fibonacci sequence |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2021-01-01 |
| description |
Abstract Recently, Bednarz introduced a new two-parameter generalization of the Fibonacci sequence, which is called the ( k , p ) $(k,p)$ -Fibonacci sequence and denoted by ( F k , p ( n ) ) n ≥ 0 $(F_{k,p}(n))_{n\geq0}$ . In this paper, we study the geometry of roots of the characteristic polynomial of this sequence. |
| topic |
Generalized Fibonacci sequence Characteristic polynomial Eneström–Kakeya theorem Descartes’ sign rule |
| url |
https://doi.org/10.1186/s13662-020-03186-8 |
| work_keys_str_mv |
AT paveltrojovsky onthecharacteristicpolynomialofkpkpfibonaccisequence |
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