p-linear schemes for sequences modulo pr

Frits Beukers

doi:10.1016/j.indag.2023.12.003

p-linear schemes for sequences modulo p^r

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Many interesting combinatorial sequences, such as Apéry numbers and Franel numbers, enjoy the so-called Lucas property modulo almost all primes p. Modulo prime powers p^r such sequences have a more complicated behaviour which can be described by matrix versions of the Lucas property called p-linear schemes. They are generalizations of finite p-automata. In this paper we construct such p-linear schemes and give upper bounds for the number of states which, for fixed r, do not depend on p.

Original language	English
Pages (from-to)	698-707
Number of pages	10
Journal	Indagationes Mathematicae
Volume	35
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2023.12.003
Publication status	Published - Jul 2024

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)

Funding

Many thanks to Armin Straub for the stimulating discussions I had on the subject of this paper and his encouragement. Many thanks also to the referee for the careful reading of this paper and for the remarks that very much improved its exposition.

Keywords

Combinatorial sequence
Lucas property
p-automata

Access to Document

10.1016/j.indag.2023.12.003Licence: CC BY

1-s2.0-S0019357723001064-mainFinal published version, 284 KBLicence: CC BY

Cite this

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