Recurrence relations, succession rules and the positivity problem
نویسندگان
چکیده
منابع مشابه
Recurrence Relations, Succession Rules, and the Positivity Problem
In this paper we present a method to pass from a given recurrence relation with constant coefficients (in short, a C-finite recurrence) to a finite succession rule defining the same number sequence. Our method consists in two steps: first, we transform the given recurrence relation into an extended succession rule, then we provide a series of operations to reduce such an extended succession rul...
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In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently studied tool for the enumeration of combinatorial objects related to the ECO method. We also discuss the applicability of our method as a test for the positivity ...
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The notion of succession rule (system for short) provides a powerful tool for the enumeration of many classes of combinatorial objects. Often, different systems exist for a given class of combinatorial objects, and a number of problems arise naturally. An important one is the equivalence problem between two different systems. In this paper, we show how to solve this problem in the case of syste...
متن کاملOn the Positivity Problem for Simple Linear Recurrence Sequences,
Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.
متن کاملThe Positivity Set of a Recurrence Sequence
We consider real sequences (fn) that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive dominating characteristic root, we establish that the density is positive. Furthermore, we determine the values that can occur as density of such a positivity set, both...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2019
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2016.09.006