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On the General Solution of the Heideman–Hogan Family of Recurrences

Hone, Andrew N.W., Ward, Chloe (2018) On the General Solution of the Heideman–Hogan Family of Recurrences. Proceedings of the Edinburgh Mathematical Society, . ISSN 0013-0915. (doi:10.1017/S0013091518000196)

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https://doi.org/10.1017/S0013091518000196

Abstract

We consider a family of nonlinear rational recurrences of odd order which was introduced by Heideman and Hogan, and recently rediscovered in the theory of Laurent phenomenon algebras (a generalization of cluster algebras). All of these recurrences have the Laurent property, implying that for a particular choice of initial data (all initial values set to 1) they generate an integer sequence. For these particular sequences, Heideman and Hogan gave a direct proof of integrality by showing that the terms of the sequence also satisfy a linear recurrence relation with constant coefficients. Here we present an analogous result for the general solution of each of these recurrences.

Item Type: Article
DOI/Identification number: 10.1017/S0013091518000196
Uncontrolled keywords: nonlinear recurrence; Laurent property; linearization
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 22 Aug 2018 13:33 UTC
Last Modified: 29 May 2019 21:02 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/68768 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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