A family of linearizable recurrences with the Laurent property. (17th March 2014)

• Record Type: Journal Article
• Authors: Hone, A. N. W.; Ward, C.
• Is Part Of: Bulletin of the London Mathematical Society. Volume 46:Part 3(2014:Jun.)
• Page Start: 503
• Page End: 516
• Publication Date: 2014-03-17
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bdu004
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract : 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.