Degree $k$ linear recursions $\mod(p)$ and number fields
نویسندگان
چکیده
منابع مشابه
DEGREE-k LINEAR RECURSIONS MOD(p) AND NUMBER FIELDS
Linear recursions of degree k are determined by evaluating the sequence of Generalized Fibonacci Polynomials, {Fk,n(t1, ..., tk)} (isobaric reflects of the complete symmetric polynomials) at the integer vectors (t1, ..., tk). If Fk,n(t1, ..., tk) = fn, then fn − k ∑ j=1 tjfn−j = 0, and {fn} is a linear recursion of degree k. On the one hand, the periodic properties of such sequences modulo a pr...
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(1.1) an = c1an−1 + c2an−2 + · · ·+ cdan−d for all n ≥ d. For example, the Fibonacci sequence {Fn} = (0, 1, 1, 2, 3, 5, 8, . . . ) is defined by the linear recursion Fn = Fn−1+Fn−2 with initial values F0 = 0 and F1 = 1. (Often F0 is ignored, but the values F1 = F2 = 1 and the recursion force F0 = 0.) We will assume cd 6= 0 and then say the recursion has order d; this is analogous to the degree ...
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For any field k and any integers m,n with 0 6 2m 6 n + 1, let Wn be the k-vector space of sequences (x0, . . . , xn), and let Hm ⊆ Wn be the subset of sequences satisfying a degree-m linear recursion, i.e. for which there exist a0, . . . , am ∈ k such that
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2011
ISSN: 0035-7596
DOI: 10.1216/rmj-2011-41-4-1303