title: Multivariate linear recurrences and power series division.
abstract: Bousquet-Mélou and Petkovšek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their results by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the case of recurrences with polynomial coefficients can be treated in an analogous way.
authors.affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Wien, Austria ; Institut für Mathematik, Technikerstraße 13, Universität Innsbruck, A-6020, Austria.
authors.forename: Herwig
authors.initials: H
authors.lastname: Hauser
authors.forename: Christoph
authors.initials: C
authors.lastname: Koutschan
keywords: Formal power series; Linear recurrence equation; Multivariate sequence; Perfect operator; Power series division; [Formula: see text]-finite recurrence