IMI/Publicaţii/CSJM/Ediţii/CSJM v.11, n.1 (31), 2003/

The splitting method and Poincare's theorem: (II) - matrix, polynomial and language

Authors: M. Margenstern
Keywords: Hyperbolic tessellations, algorithmic approach.


This paper is the continuation of the paper which appeared in the previous issue: we revisited Poincare's theorem in the light of the splitting method which was introduced by the author in [5], especially in the geometric aspect of the question.

This new part is also based on the definition of a combinatoric tiling which was detailed in the previous issue. Indeed, this definition has a natural algebraic continuation as long as it involves a matrix, hence a polynomial. We discuss here the connection of these objects which we provide the reader in full extent, with the notion of languages which are attached in such a case which we call the language of the splitting.

We show that in all the cases under study, the language of the splitting is not regular.

Maurice Margenstern
LITA, EA 3097,
Universite de Metz,
Ile du Saulcy,
57045 Metz Cedex, France


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