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A family of linearizable recurrences with the Laurent property

Hone, Andrew N.W., Ward, Chloe (2014) A family of linearizable recurrences with the Laurent property. Bulletin of the London Mathematical Society, 46 (3). pp. 503-516. ISSN 0024-6093. (doi:10.1112/blms/bdu004) (KAR id:41483)


We consider a family of non-linear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced recently by Lam and Pylyavskyy. Furthermore, each member of this family is shown to be linearizable in two different ways, in the sense that its iterates satisfy both a linear relation with constant coefficients and a linear relation with periodic coefficients. Associated monodromy matrices and first integrals are constructed, and the connection with the dressing chain for Schrödinger operators is also explained.

Item Type: Article
DOI/Identification number: 10.1112/blms/bdu004
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 20 Jun 2014 23:07 UTC
Last Modified: 08 Dec 2022 18:11 UTC
Resource URI: (The current URI for this page, for reference purposes)

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