Explicit polynomial generators for the ring of quasi-symmetric functions over the integers

Abstract

In [5, 6] it has been proved that the ring of quasisymmetric functions over the integers is free polynomial, see also [4]. This is a matter that has been of great interest since 1972; for instance because of the role this statement plays in a classification theory for noncommutative formal groups that has been in development since then, see [2] and [9] and the references in the latter. Meanwhile quasisymmetric functions have found many more aplications, [3]. However, the proofs in [5, 6] do not give explicit polynomial generators for QSymm over the integers. In this note I give a (really quite simple) set of polynomial generators for QSymm over the integers.