Abstract
Germsof Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (ESAIM Control Optim Calc Var. 1:241–266, 1996) and Mormul (Cent Eur J Math 2:859–883, 2004) have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii (Mem Amer Math Soc 203(956):x+137, 2010) have shown that such germs correspond to finite jets of Legendrian curve germs, and that the RVT coding corresponds to the classical invariant in the singularity theory of planar curves: the Puiseux characteristic. Here, we derive a simple formula, Theorem 2, for the Puiseux characteristic of the curve corresponding to a Goursat germ with given small growth vector. The simplicity of our theorem (compared with the more complex algorithms previously known) suggests a deeper connection between singularity theory and the theory of nonholonomic distributions.