An extension of holonomic sequences: C2-finite sequences

Jiménez-Pastor, Antonio; Nuspl, Philipp; Pillwein, Veronika

doi:10.1016/j.jsc.2022.10.008

Cited by 3 publications

(5 citation statements)

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“…Several examples for C 2 -finite sequences are given in [29,9]. Throughout this article, additional examples are given.…”

Section: -Finite Sequencesmentioning

confidence: 99%

“…Previously, it was shown that C 2 -finite sequences, analogously to C-finite sequences, form a K-algebra and they are furthermore closed under taking subsequences at arithmetic progressions and interlacing [8,9]. So far, it was not known whether these closure properties can be computed effectively.…”

Section: -Finite Sequencesmentioning

confidence: 99%

“…Note that in [8,9] it is assumed that the leading coefficient c r in (2) has no zero terms at all. The two definitions are equivalent.…”

Section: -Finite Sequencesmentioning

confidence: 99%

“…The computation of closure properties of C 2 -finite sequences can be reduced to solving linear systems of equations [8,9]. A C 2 -finite recurrence…”

Section: Order Boundsmentioning

confidence: 99%

“…It has been shown [8,9,24,22] that many of these closure properties also hold and can be implemented for sequences that are defined by linear recurrences with C-finite coefficients, also called C 2 -finite. To our knowledge, C 2 -finite sequences have first been introduced formally by Kotek and Makowsky [14] in the context of graph polynomials.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Order bounds for $C^2$-finite sequences

Kauers¹,

Nuspl²,

Pillwein³

2023

Preprint

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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.

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“…Several examples for C 2 -finite sequences are given in [29,9]. Throughout this article, additional examples are given.…”

Section: -Finite Sequencesmentioning

confidence: 99%

Section: -Finite Sequencesmentioning

confidence: 99%

“…Note that in [8,9] it is assumed that the leading coefficient c r in (2) has no zero terms at all. The two definitions are equivalent.…”

Section: -Finite Sequencesmentioning

confidence: 99%

“…The computation of closure properties of C 2 -finite sequences can be reduced to solving linear systems of equations [8,9]. A C 2 -finite recurrence…”

Section: Order Boundsmentioning

confidence: 99%