Une description combinatoire du sous-groupe principal de congruence Γ(2) de SL(2, Z)

Abstract

We characterize sequences of positive integers (c 1 , c 2 , ..., cn) for which the (2 × 2)-matrix c 1 −1 1 0 · · · cn −1 1 0 belongs to the principal congruence subgroup of level 2 in SL(2, Z). The answer is given in terms of dissections of a convex n-gon into a mixture of triangles and quadrilaterals.