| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-02-03T11:12:02Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151511 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
