Degree k Linear Recursions Mod(p)
| dc.creator | MacHenry, Trueman | |
| dc.creator | Wong, Kieh | |
| dc.date | 2007-12-14 | |
| dc.date.accessioned | 2026-07-07T08:49:20Z | |
| dc.date.available | 2026-07-07T08:49:20Z | |
| dc.description | Linear recursions of degree $k$ are determined by evaluating the sequence of Generalized Fibonacci Polynomials, $\{F_{k,n}(t_1,...,t_k)\}$ (isobaric reflects of the complete symmetric polynomials) at the integer vectors $(t_1,...,t_k)$. If $F_{k,n}(t_1,...,t_k) = f_n$, then $$f_n - \sum_{j=1}^k t_j f_{n-j} = 0,$$ and $\{f_n\}$ is a linear recursion of degree $k$. On the one hand, the periodic properties of such sequences modulo a prime $p$ are discussed, and are shown to be rela ted to the prime structure of certain algebraic number fields; for example, the arithmetic properties of the period ar e shown to characterize ramification of primes in an extension field. On the other hand, the structure of the semiloca l rings associated with the number field is shown to be completely determined by Schur-hook polynomials. | |
| dc.description | 28 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0712.2403 | |
| dc.identifier | http://arxiv.org/abs/0712.2403 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144260 | |
| dc.subject | Number Theory | |
| dc.subject | 05E05, 11S99 | |
| dc.title | Degree k Linear Recursions Mod(p) | |
| dc.type | text |