| Title:
|
On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions (English) |
| Author:
|
Bród, Dorota |
| Author:
|
Szynal-Liana, Anetta |
| Author:
|
Włoch, Iwona |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
1239-1248 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. (English) |
| Keyword:
|
Jacobsthal number |
| Keyword:
|
Jacobsthal-Lucas number |
| Keyword:
|
quaternion |
| Keyword:
|
generalized quaternion |
| Keyword:
|
Binet formula |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| idZBL:
|
Zbl 07655798 |
| idMR:
|
MR4517611 |
| DOI:
|
10.21136/CMJ.2022.0174-22 |
| . |
| Date available:
|
2022-11-28T11:46:11Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151145 |
| . |
| Reference:
|
[1] Çimen, C. B., İpek, A.: On Pell quaternions and Pell-Lucas quaternions.Adv. Appl. Clifford Algebr. 26 (2016), 39-51 \99999DOI99999 10.1007/s00006-015-0571-8 . Zbl 1344.11022, MR 3459988, 10.1007/s00006-015-0571-8 |
| Reference:
|
[2] Halici, S.: On Fibonacci quaternions.Adv. Appl. Clifford Algebr. 22 (2012), 321-327. Zbl 1329.11016, MR 2930698, 10.1007/s00006-011-0317-1 |
| Reference:
|
[3] Horadam, A. F.: Complex Fibonacci numbers and Fibonacci quaternions.Am. Math. Mon. 70 (1963), 289-291. Zbl 0122.29402, MR 0146137, 10.2307/2313129 |
| Reference:
|
[4] Horadam, A. F.: Jacobsthal and Pell curves.Fibonacci Q. 26 (1988), 77-83. Zbl 0644.10014, MR 0931426 |
| Reference:
|
[5] Horadam, A. F.: Jacobsthal representation numbers.Fibonacci Q. 34 (1996), 40-54. Zbl 0869.11013, MR 1371475 |
| Reference:
|
[6] Iyer, M. R.: A note on Fibonacci quaternions.Fibonacci Q. 7 (1969), 225-229. Zbl 0191.32701, MR 0255513 |
| Reference:
|
[7] Szynal-Liana, A., Włoch, I.: A note on Jacobsthal quaternions.Adv. Appl. Clifford Algebr. 26 (2016), 441-447. Zbl 1335.11095, MR 3460010, 10.1007/s00006-015-0622-1 |
| Reference:
|
[8] Szynal-Liana, A., Włoch, I.: The Pell quaternions and the Pell octonions.Adv. Appl. Clifford Algebr. 26 (2016), 435-440. Zbl 1344.11027, MR 3460009, 10.1007/s00006-015-0570-9 |
| Reference:
|
[9] Szynal-Liana, A., Włoch, I.: Generalized commutative quaternions of the Fibonacci type.Bol. Soc. Mat. Mex., III. Ser. 28 (2022), Article ID 1, 9 pages. Zbl 1479.11040, MR 4343010, 10.1007/s40590-021-00386-4 |
| Reference:
|
[10] Tasci, D.: On $k$-Jacobsthal and $k$-Jacobsthal-Lucas quaternions.J. Sci. Arts 3 (2017), 469-476. |
| . |
