Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ of characteristic 0. Then the ring of symmetric polynomials in $R$ is generated (as a $K$-algebra) by the minimal generators $e_i$ for $i=1,...,n$ where $e_i$ are the elementary symmetric polynomials, see https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial. There are also other well known minimal generators such as the power sum symmetric polynomials.
Question: What is known about minimal generators of the ring of quasi-symmetric polynomials in R?
Im looking for a good reference that answers this question.
Is there also an explicit list of $n$ minimal generators for the ring of quasi-symmetric polynomials and can they be obtained for a fixed $n$ using Sage?