| Title:
|
On a binary recurrent sequence of polynomials (English) |
| Author:
|
Euler, Reinhardt |
| Author:
|
Gallardo, Luis H. |
| Author:
|
Luca, Florian |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
22 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
151-157 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the properties of the sequence of polynomials given by $g_0=0,~g_1=1$, $g_{n+1}=g_n+\Delta g_{n-1}$ for $n\ge 1$, where $\Delta \in {\mathbb F}_q[t]$ is non-constant and the characteristic of ${\mathbb F}_q$ is $2$. This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219. (English) |
| Keyword:
|
sequences of binary polynomials |
| Keyword:
|
Stern-Brocot sequence |
| Keyword:
|
perfect fields of characteristic 2 |
| MSC:
|
11B39 |
| MSC:
|
11T06 |
| MSC:
|
11T55 |
| idZBL:
|
Zbl 06410232 |
| idMR:
|
MR3303136 |
| . |
| Date available:
|
2015-01-27T09:38:19Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144128 |
| . |
| Reference:
|
[1] Cherly, J., Gallardo, L., Vaserstein, L., Wheland, E.: Solving quadratic equations over polynomial rings of characteristic two.Publ. Math., 42, 1998, 131-142, Zbl 0915.13017, MR 1628154, 10.5565/PUBLMAT_42198_06 |
| Reference:
|
[2] Euler, R., Gallardo, L.H.: On explicit formulae and linear recurrent sequences.Acta Math. Univ. Comenianae, 80, 2011, 213-219, Zbl 1255.11061, MR 2835276 |
| Reference:
|
[3] He, T.-X., Shiue, P.J.-S.: On sequences of numbers and polynomials defined by linear recurrence relations of order 2.Int. J. Math. Math, Sci., 2009, Art. ID 709386, 21 pp.. Zbl 1193.11014, MR 2552555 |
| Reference:
|
[4] Northshield, S.: Stern's diatomic sequence $0,1,1,2,1,3,2,3,1,4,...$.Amer. Math. Monthly, 117, 2010, 581-598, Zbl 1210.11035, MR 2681519, 10.4169/000298910X496714 |
| Reference:
|
[5] Sloane, N.J.A.: OEIS.https://oeis.org/. |
| . |
