A short proof of a Gauss problem

Hubert de Fraysseix (1) , Patrice Ossona de Mendez (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

The traversal of a self crossing closed plane curve, with points of multiplicity at most two, defines a double occurrence sequence. C.F. Gauss conjectured that such sequences could be characterized by their interlacement properties. This conjecture was proved by P. Rosenstiehl in 1976. We shall give here a simple self-contained proof of his characterization. This new proof relies on the D-switch operation.

Mots clés: Gauss code

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez. A short proof of a Gauss problem. 1997, pp.230-235. ⟨hal-00005636⟩