A family of linearizable recurrences with the Laurent property

作者：Hone A N W^*; Ward C

来源：Bulletin of the London Mathematical Society, 2014, 46(3): 503-516.

DOI：10.1112/blms/bdu004

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 Schrodinger operators is also explained.

• 出版日期2014-6