Kneading determinants of infinite order linear recurrences
نویسندگان
چکیده
منابع مشابه
Linear Recurrences of Order Two
where the A{ are rational integers, is called an integral linear recurrence of order k. Given such a linear recurrence and an integer c, one would like to know for what n does f(n) — c? In a very few particular instances (e.g. see [2], [6]) this question has been answered, but in general the question is very difficult. A less exacting problem is the determination of upper and lower bounds on th...
متن کاملThe Generation of Higher-order Linear Recurrences from Second-order Linear Recurrences
Along the lines of this theorem, Selmer [1] has shown how one can form a higher-order linear recurrence consisting of the term-wise products of two other linear recurrences. In particular, let {sn} be an m-order and {tn} be a p-order linear integral recurrence with the associated polynomials s(x) and t(x), respectively. Let a^, i = 1,2, ..., m, and 3j, j = 1, 2, ..., p, be the roots of the poly...
متن کاملExpressing Reachability in Linear Recurrences, as Infinite Determinants and Rational Polynomial Equations
We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the i term in a non-Homogenous Linear Recurrence. We use this to derive the infinite determinant that is zero, if and only if, the desired rational can be reached by some term in the recurrence. Second, we de...
متن کاملSecond-order Linear Recurrences of Composite Numbers
In a well-known result, Ronald Graham found a Fibonacci-like sequence whose two initial terms are relatively prime and which consists only of composite integers. We generalize this result to nondegenerate second-order recurrences.
متن کاملOn Rationality of Kneading Determinants
In this section, R denotes a ring with identity I. We study conditions under which I - Aλ and I - Bλ are left coprime or right coprime, where A, B ∈ R. As applications, we get sufficient conditions under which the Kneading determinant of a finite rank pair of operators on an infinite dimensional space is rational.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.02.035