One of the remarkable properties of cluster algebras is that any cluster, obtained from a
sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the …

Abstract Birational toggling on Gelfand–Tsetlin patterns appeared first in the study of
geometric crystals and geometric Robinson–Schensted–Knuth correspondence. Based on …

Following van der Poorten, we consider a family of nonlinear maps that are generated from
the continued fraction expansion of a function on a hyperelliptic curve of genus g. Using the …

In recent work it was shown how recursive factorisation of certain QRT maps leads to Somos-
4 and Somos-5 recurrences with periodic coefficients, and to a fifth-order recurrence with the …

This thesis deals with applications of experimental mathematics to a variety of fields. The first
is partition identities. These identities, such as the Rogers-Ramanujan identities, are …

Many discrete integrable systems exhibit the Laurent phenomenon. In this paper, we
investigate three integrable systems: the Somos-4 recurrence, the Somos-5 recurrence, and …

We generalise the expansion formulae of Musiker, Schiffler and Williams, obtained for
cluster algebras from orientable surfaces, to a larger class of coefficients which we call …

Элементарный подход к изучению последовательностей Сомоса Page 1 ТРУДЫ
МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. ВАСТЕКЛОВА, 2019, т. 305, с. 330–343 УДК …

We show how to obtain relations for the divisors of terms generated by a homogenized
version of a rational recurrence. When the rational recurrence confines singularities the …

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 …