Free polynomial generators for the Hopf algebra QSym of quasisymmetric functions Original Research Article

In the proof of [11, Corollary 2], of Malvenuto and Reutenauer showed that the set of Lyndon words image in the language over the alphabet of positive integers is a set of free polynomial generators for the ring imageimage of quasisymmetric functions over the field image of rational numbers. A slight modification of the definition of Lyndon words permits to present a set of free polynomial generators for the ring image of quasisymmetric functions over the ring of rational integers image.