Abstract: In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation.

In this talk I report on joint work with L.S. Krapp and S. Kuhlmann where we introduce the notion of generalised linear recurrence relations for power series with exponents in an arbitrary ordered abelian group generalising Kronecker’s original result.

Moreover, we study distinguished subfields of a power series field, which are determined by generalised linear recurrence relations.