Article
| Title: | Root location for the characteristic polynomial of a Fibonacci type sequence (English) |
| Author: | Du, Zhibin |
| Author: | da Fonseca, Carlos M. |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 189-195 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We analyse the roots of the polynomial $x^n-px^{n-1}-qx-1$ for $p\geqslant q\geqslant 1$. This is the characteristic polynomial of the recurrence relation $F_{k,p,q}(n) = pF_{k,p,q}(n- \nobreak 1) + qF_{k,p,q}(n-k + 1) + F_{k,p,q}(n-k)$ for $n \geqslant k$, which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided. (English) |
| Keyword: | Fibonacci number |
| Keyword: | root |
| Keyword: | characteristic polynomial |
| MSC: | 11A63 |
| MSC: | 11B39 |
| MSC: | 11J86 |
| idZBL: | Zbl 07655762 |
| idMR: | MR4541096 |
| DOI: | 10.21136/CMJ.2022.0043-22 |
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| Date available: | 2023-02-03T11:12:02Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151511 |
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