Let C[[z]] be the ring of formal power series and C((z)) the field of formal Laurent power series, the field of fractions of C[[z]]. Given a complex algebraic group G, we will write G((z)) for the group of C((z))-rational points of G, thought of as a formal “loop group,” and a(z) for an element of G((z)). Let q be a fixed nonzero complex number. Define a “twisted” conjugation action of G((z)) o...

The purpose behind this work is to construct from a family of algebraic formal power series of degree more than 2, a family of transcendental fractions over IKp(X).

We give a survey of recent works relating algebraic languages and formal power series with the enumeration of polyominoes (and animals). More precisely, encoding these structures with words yields new exact results.

In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there is evidence that the weaker concept is enough for many computational purposes. We give a detailed study of the Jung method and show how it facilitates an eff...