DeepAI AI Chat
Log In Sign Up

Order bounds for C^2-finite sequences

by   Manuel Kauers, et al.

A sequence is called C-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with C-finite coefficients. Recently, it was shown that such C^2-finite sequences satisfy similar closure properties as C-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of C^2-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.


page 1

page 2

page 3

page 4


Performance Limits of Lattice Reduction over Imaginary Quadratic Fields with Applications to Compute-and-Forward

In this work, we first examine both Hermite's constant and Minkowski's t...

Factorization of C-finite Sequences

We discuss how to decide whether a given C-finite sequence can be writte...

D-finite Numbers

D-finite functions and P-recursive sequences are defined in terms of lin...

The Membership Problem for Hypergeometric Sequences with Quadratic Parameters

Hypergeometric sequences are rational-valued sequences that satisfy firs...

Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals

In this paper, we give decision criteria for normal binomial difference ...

Connecting 3-manifold triangulations with monotonic sequences of bistellar flips

A key result in computational 3-manifold topology is that any two triang...


In this paper we introduce a new formulation of Bennett's logical depth ...